A reconstruction of the tables of
Briggs’ Arithmetica logarithmica
(1624)
Denis Roegel
11 January 2011
(last version: 30 november 2014)
This document is part of the LOCOMAT project:
http://locomat.loria.fr
I ever rest a lover of all them that love the Mathematickes
Henry Briggs, preface to [69]
1
Briggs’ first table of logarithms (1617)
Henry Briggs (1561–1631)1 is the author of the first table of decimal logarithms, published
in 1617, of the first extensive table of decimal logarithms of numbers (1624), and of the
first extensive table of decimal logarithms of trigonometric functions (1633).
After having been educated in Cambridge, Briggs became in 1596 the first professor
of geometry at Gresham College, London [107, p. 120], [96, p. 20], [119]. Gresham College was England’s scientific centre for navigation, geometry, astronomy and surveying.2
Briggs stayed there until 1620, at which time he went to Oxford, having been appointed
the first Savilian Professor of Geometry in 1619 [96, p. 24].
While at Gresham College, Briggs became friends with Edward Wright. He also seems
to have spent time doing research in astronomy and navigation [96, pp. 29–30]. Briggs had
in particular published several tables for the purpose of navigation in 1602 and 1610 [120].
Several of Briggs’ tables were published under the name of others [96, p. 8].3
In 1614, John Napier (1550–1617) published his Mirifici logarithmorum canonis descriptio, the description of his table of logarithms [68, 89]. It is through this work that
Briggs was early exposed to the theory of logarithms. After Napier’s publication, Briggs
went to visit him in Scotland in the summers of 1615 and 1616 and they agreed on the
need to reformulate the logarithms, a task that Briggs took over.
Briggs published his first table of decimal logarithms in 1617 [9, 82]. It was a small
booklet of 16 pages, of which the first page was an introduction, and the remaining 15
pages were tables. Briggs’ table gave the decimal logarithms of the integers 1 to 1000 to
14 places.
The Arithmetica logarithmica (1624)
2
Seven years after his first table of logarithms, Briggs published his Arithmetica logarithmica which gave the logarithms of the numbers from 1 to 20000 and from 90001 to
100000 with 14 decimals [10].4
Some copies of Briggs’ table also contain an appendix with the logarithms of the
interval 100000–101000, but as we haven’t seen it, we do not reproduce it here.5 For a
description of these extra sheets and their use, see Malcolm [61, pp. 303–305].
1
Briggs was baptized on February 23, 1560 (old style), which is 1561 new style. He died on January
26, 1630 (old style), which is 1631 new style [51].
2
Gresham College was a very fluctuating institution, and the main reason for its claim to scientific
responsability was the work and influence of Briggs. The flourishing period of Gresham College ended
with the death of Henry Gellibrand in 1636 [2, p. 20].
3
For more biographical information on Briggs, consult Smith [94], Ward [107], Sonar [96] and Kaunzner [52]. Sonar gives an overview of Briggs’ works prior to his tables of logarithms [96].
4
A copy of the Arithmetica logarithmica can be found on google books (id: L88WAAAAQAAJ).
5
One example, among others, is appended alone to the French edition of Vlacq’s Arithmetica logarithmica located at the Harald Cohen Library of the University of Liverpool (call number SPEC
RYL.P.2.12) [29].
3
Although scarce now, it seems that Briggs’ book was printed in (relatively) too many
copies, so that it could be obtained in the streets of London for a very small price [36,
pp. 381–382].
3
Briggs’ methods
In order to compute decimal logarithms, Briggs considered several methods, each method
making it possible for him to move a step further.6
3.1
Square roots
A straightforward way to compute new logarithms from existing ones is√to use the square
. The
root. For instance, if log n = a and log m = b are known, then log mn = a+b
2
use of square roots had already been alluded to by Napier in his Construction, to which
Briggs added some comments [72].7
√
n
Briggs used this method as follows. He first considered the logarithms of 2 10. Their
values are actually very easy to compute:
log 10 = 1
√
log 10 = 0.5
√
4
log 10 = 0.25
......
√
2n
log 10 = 2−n
Briggs computed these values until n = 54, with 32 decimal places for the last values
of the roots and 40 decimal places for the last values of the logarithms [10, pp. 10–11].
The last entries of his table are
1
10 252 = 1.00000 00000 00000 51127 65972 80129 47
1
10 253 = 1.00000 00000 00000 25563 82986 40064 70
1
10 254 = 1.00000 00000 00000 12781 91493 20032 35
whose logarithms are
1
= 0.00000 00000 00000 22204 46049 25031 30808 47263
252
1
= 0.00000 00000 00000 11102 23024 62515 65404 23631
253
1
= 0.00000 00000 00000 05551 11512 31257 82702 11815.
254
6
Various overviews of Briggs’ methods have been published, for instance by Delambre [20], Hutton [48],
and others [26, 25], and the reader is directed to our bibliography for further information.
7
Some authors have oversimplified Briggs’ method and presented Napier’s use of square roots as
Briggs’, see for instance Abellan [1]. On the other hand, it is obvious that Briggs’ methods were the
results of Napier’s and Briggs’ exchanges during Briggs’ visits to Scotland.
4
√
n
Briggs stopped extracting roots as soon as the digits of 2 10 after the unit were
exactly halved from one root to the next. Briggs in fact computed some decimals more,
but his main table contains the values above. The number of significative digits of the
last square root after the zeros is slightly more than the 15 digits Briggs needed for his
table.
Briggs realized that when x = 1 + r is close to 1, then log x ≈ αr, where α is some
proportionality factor that he sought to determine.8 By a mere proportion (the so-called
“golden rule”), Briggs found that
α≈
55511151231257827021181583
≈ 0.434294481903251804.
127819149320032344165000000
Briggs’ result is correct given the two values he divided, but it is only accurate to 16
places with respect to the value sought which is
1
= 0.43429448190325182765 . . .
ln 10
√
n
Now, if 2 x = 1 + r and log(1 + r) ≈ αr, then log x ≈ 2n αr and this gives a way to
compute the logarithm of x, by successive square root extractions.
The accuracy of the result can easily be estimated. Let r0 and α0 be the significative
parts of r and α. We can assume 0.1 ≤ r0 < 1 and 0.1 ≤ α0 < 1. If r0 and α0 have 18
exact (rounded) significative digits, the error on each value is less than 5 · 10−19 , hence
their product will be wrong by at most 10−18 . The product will have more than 16 exact
(rounded) significative digits and usually at least 17. Since 2n is computed exactly, log x
can be computed with 17 exact (rounded) significative digits.
Of course, computing these square roots was tedious. It will therefore not be a surprise
to discover that Briggs made a computation error in his 54 square root extractions, but
this error happened to have no consequences, contrary to Napier’s error in the construction of his tables. It must also be observed √
that Briggs computed the roots with more
decimals than he really needed. His value of 10 was given to 26 decimal places, but he
would have obtained
17
√ the same final digits for the 54th√root if he had kept only about
−17
decimal places of 10. This follows easily if we write 10 = a + b, where b < 10 :
10
We have
1
254
= (a + b)
1
253
=a
1
253
b
1+
a
1
253
=a
1
253
1 b
1 + 53 + · · ·
2 a
1 b
< 3.51 . . . · 10−33
253 a
1
and therefore there are about 33 correct decimal places in a 253 which is what Briggs
eventually obtains. A more detailed analysis of Briggs’ errors is given by Ian Bruce in
his notes to the translation of the Arithmetica logarithmica.9
8
Whiteside’s account in that respect is historically inaccurate, as he writes that Briggs observed that
for small x, loge (1 + x) ≈ x [109, p. 10].
9
See http://www.17centurymaths.com.
5
3.2
Shortcuts and logarithms of the first primes
After the first series of square root extractions, Briggs continued with the computation of
log 2 [10, pp. 12–15]. He introduced a faster method. Instead of starting with the square
root of 2, he found a power of 2 which was close to a power of 10. He took 1024 = 210
and divided this number by 1000. Then, he computed the logarithm of 1.024 using the
method of the previous section. He extracted the root 47 times and obtained
1.00000 00000 00000 16851 60570 53949 77
the exact value being
1.00000 00000 00000 16851 60570 53949 7663 . . .
The 47th square root is in the area in which Briggs considers that log(1 + x) ≈ αx. If
Briggs had started with 2, he would have extracted the square root 52 times, so in this
case he was able to save five square root extractions.
Once Briggs had the last square root, he could compute the value of the logarithm
using α and the “golden rule.” He found
0.00000 00000 00000 07318 55936 90623 9368
the exact value being
0.00000 00000 00000 07318 55936 90623 933137
From that, Briggs obtained
log 1.024 ≈ 0.01029 99566 39811 95265 27744
and then
log 1024 ≈ 3.01029 99566 39811 95265 27744
and this is 10 log 2, hence
log 2 ≈ 0.30102 99956 63981 19526 527744
This value is correct to 19 decimal places.
Once Briggs had the value of log 2, he easily obtained log 5, given that log 1, log 2,
and log 10 were known: log 10 − log 5 = log 2, hence
log 5 = 1 − log 2 ≈ 0.69897 00043 36018 805
Briggs then computed log 3. He started with 69 = 10077696 and applied the method
which he used to compute log 2. Eventually, he found log 6 ≈ 0.77815 12503 83643 63 and
log 3 = log 6 − log 2 ≈ 0.47712 12547 19662 44.
6
3.3
The use of finite differences
In the next chapter of the Arithmetica logarithmica, Briggs expounds another method
in order to ease the computation of the square roots [10, pp. 15–17].10 After having
extracted many roots, Briggs obviously noticed some patterns. Using modern notations,
√
√
we can easily express them. Let y0 be the initial number, y1 = y0 , y2 = y1 , etc. Then,
we set yn = 1 + An . Briggs called the values of An the first differences.11
As shown above, Briggs had noticed that
√ when An isx small, log yn ≈ αAn . Moreover,
An
An+1 ≈ 2 . This of course follows from 1 + x = 1 + 2 + · · · , but Briggs didn’t know
this series expansion.
Once this pattern had been noticed, it was natural to see how much An+1 was differing
from A2n , and therefore Briggs considered the “second” 12 differences Bn+1 = A2n − An+1 .
Briggs then noticed that Bn+1 ≈ B4n . In other words, Briggs noticed that
y
−1
n−1
− (yn − 1)
yn − 1
2
− (yn+1 − 1) ≈
2
4
2
√
This follows easily, if we set yn−1 = 1 + x. Then, yn = yn−1 = 1 + x2 − x8 + · · · and
2
√
+ · · · , and the previous approximation is equivalent to
yn+1 = yn = 1 + x4 − 3x
32
x 3x2
x x2
x
x x2
2
2
2
−
+ o(x ) −
−
+ o(x ) ≈ −
−
+ o(x )
4 16
4
32
8
8 32
x2
x2
2
+ o(x ) ≈
+ o(x2 )
32
32
but Briggs still only had an experimental approach.
Briggs then went on and considered the third differences Cn+1 = B4n − Bn+1 and he
noticed that Cn+1 ≈ C8n . Afterwards, he noticed that Dn+1 ≈ D24n , En+1 ≈ E25n , etc. But
he did not prove this result.
3.3.1
Developments of
√
1+x
If we set x = An , we have
√
1 + x = 1 + An+1
1
= 1 + An − Bn+1
2
1
1
= 1 + An − Bn + Cn+1
2
4
1
1
1
= 1 + An − Bn + Cn − Dn+1
2
4
8
1
1
1
1
= 1 + An − Bn + Cn − Dn + En+1
2
4
8
16
= ···
10
An overview of Briggs’ method can be found in Sonar’s book [96, pp. 197–201]. A more detailed
analysis can be found in Hutton’s survey [48, pp. 60–73].
11
In this section, except for yn , we use Ian Bruce’s notations. Briggs actually only used A, B, C, etc.,
but following Bruce, we have added indices.
12
These are of course not the second differences in the usual sense.
7
These equations can be extended into an infinite series, but we haven’t proved that
these series converge.
We can obtain developments of Bn , Cn , Dn , etc. in terms of x. Setting f (x) =
(1 + x)2 − 1 = x2 + 2x, we have:
Bn =
Cn =
Dn =
En =
Fn =
Gn =
f (x)
x2
An−1
− An =
−x=
2
2
2
(f (x))2
x2
(x2 + 2x)2 x2
x3 x4
Bn−1
− Bn = 2 −
=
−
=
+
4
4
2
8
2
2
8
Cn−1
7x4 7x5 7x6 x7 x8
− Cn =
+
+
+
+
4
4
8
16
8
64
5
21x
+ ···
8
217x6
+ ···
16
1953x7
+ ···
16
Briggs actually gave these developments until Jn and up to the terms in x10 [10, p. 16].
1
2
3
We can analyze these expressions
as follows. Setting
n = Cn ,
√ Φn = An , Φn = Bn , Φ
Pk−1
i+1 1 i
k+1 k
etc., we define ϕ(n, k) = 1 + i=1 (−1) 2i Φn . Then 1 + x = ϕ(n, k) + (−1) Φn+1 .
As indicated by the expansions of An , Bn , etc., it seems that
for all k, Φkn = ak Φ1n
k
+ ···
(1)
That this is so is actually easy to prove.13 We can proceed by induction. Assume
k
k+1
k+2
Φkn = a (Φ1n ) + b (Φ1n )
+ c (Φ1n )
+ · · · and note that An−1 = f (An ), or, in other
1
1
words, Φn−1 = f (Φn ). Then,
1 k
Φ
− Φkn
2k n−1
k+1
k
k
k+1
1 + ···
= k a Φ1n−1 + b Φ1n−1
+ · · · − a Φ1n − b Φ1n
2
k
k+1
k
k+1
1 = k a f (Φ1n ) + b f (Φ1n )
+ · · · − a Φ1n − b Φ1n
+ ···
2 k
k+1
2 k
2 k+1
1
+ · · · − a Φ1n − b Φ1n
+ ···
+ b 2Φ1n + Φ1n
= k a 2Φ1n + Φ1n
2
i
k
k+1
k
k+1
1 h = k a 2k Φ1n + · · · + b 2k+1 Φ1n
+ · · · + · · · − a Φ1n − b Φ1n
+ ···
2
k+2
k+1
= a0 Φ1n
+ b0 Φ1n
+ ···
Φk+1
=
n
13
In his article on Briggs’ anticipation of the binomial theorem, Whiteside
√ derives the binomial expansion by grouping the terms of the developments from the expansion of 1 + x, but omitting the proof
of the property (1) of Φkn . The proof is therefore not complete. For a comparison, note that Whiteside
writes e0 for our An , e−1 for An+1 , ∆10 for Bn , ∆20 for Cn , etc., ∆1−1 for Bn+1 , ∆2−1 for Cn+1 , etc.
Whiteside’s ∆kp is our Φk+1
n−1−p [109].
8
We therefore have
Φkn
Φkn−1
≈
ak xk
ak f (x)k
=
ak xk
ak (2x)k
=
1
,
2k
which is what Briggs noticed.
xk
We also have Φkn+1 = ak 2k + · · · . and therefore ϕ(n, k) contains all the terms xi ,
for i < k. This
k) necessarily has the same development as the binomial
√ is why ϕ(n,
x
1 3
x − · · · up to xk−1 .
expansion of 1 + x = 1 + 2 − 18 x2 + 16
3.3.2
Backwards computation
Once Briggs had computed Ai , Bi , . . . , for i ≤ n, he was able to use these values
backwards to compute approximations of . . . , Cn+1 , Bn+1 , and An+1 , and therefore having
the next square root, with a less tedious computation.
√
Taking again the above developments of 1 + x, the computation would proceed as
follows:
En
25
Bn
=
− Cn+1
4
Dn
− En+1
16
An
=
− Bn+1
2
En+1 ≈
Dn+1 =
Bn+1
An+1
Cn+1 =
Cn
− Dn+1
8
Briggs applied this method when x was very small. Briggs could then compute approximations of the square roots without explicitely extracting these roots.
69
As an example, Briggs considered the extraction of the roots of 10
7 = 1.0077696 [10,
pp. 15–17]. Briggs first computed the first nine successive square roots:
√
24
√
25
√
26
√
27
√
28
√
29
......
1.0077696 = 1 + A4 = 1.00048 38402 68846 62985 49253 5
1.0077696 = 1 + A5 = 1.00024 18908 78824 68563 80872 7
1.0077696 = 1 + A6 = 1.00012 09381 26397 13459 43919 4
1.0077696 = 1 + A7 = 1.00006 04672 35055 30968 01600 5
1.0077696 = 1 + A8 = 1.00003 02331 60505 65775 96479 4
1.0077696 = 1 + A9 = 1.00001 51164 65999 05672 95048 8
Using the computed values of A4 , A5 , A6 , A7 , A8 , and A9 , Briggs computed B5 , B6 ,
C6 , B7 , C7 , D7 , B8 , C8 , D8 , E8 , and finally B9 , C9 , D9 , E9 . The latter value being
sufficiently small, the computation was then run backwards, first computing E10 ≈ E329 ,
then D10 , C10 , etc. He then obtained A10 = 1.00000 75582 04436 30121 42907 60, the
exact value being 1.00000 75582 04436 30121 42907 64 . . .. This procedure is carried out
until An+1 = A2n when restricted to Briggs’ 32 significative digits.
As mentioned above, Briggs also gave the developments in An and he suggested to
use them to compute An+1 . Using An , Briggs could compute Bn , Cn , Dn , etc., and then
compute An+1 [10, p. 16]. This process can then be repeated and the sequence of square
roots obtained.
9
3.4
Prime numbers
Using the previous methods, Briggs was able to compute the logarithms of 1, 2, 3, 5,
10 and all logarithms obtained from these by multiplication or division. Next, Briggs
considered the logarithms of prime numbers [10, pp. 17–19].
Briggs assumed that the logarithms of numbers were known up to n, and he wanted
to compute the logarithm of n + 1. In order to do so, Briggs found several arithmetical
relations involving n + 1 and integers whose logarithms are known.
For instance, in order to compute log 79, Briggs considered the products:
a = 79 × 18 = 1422,
b = 49 × 29 = 1421,
c = 71 × 20 = 1420.
2
1
b
= 1 + ac
. This number
Since a, b, and c are consecutive, we have b2 − 1 = ac and ac
is close to 1 and its logarithm can be computed with the first method. From that, log 79
follows.
Briggs used this method to compute the logarithms of the primes up to 97. In the
Arithmetica logarithmica, he gave all the triples (a, b, c) that he used [10, p. 18].
3.5
Fractions
In the chapter 10 of the Arithmetica logarithmica [10, pp. 19–21], Briggs considers the
logarithms of fractions and obtains the equivalent of log ab = log a − log b, or, in Briggs’
words, “if the logarithm of the denonimator is taken from the logarithm of the numerator,
there remains the logarithm of the fraction.” 14
3.6
3.6.1
Subtabulation
Subtabulation using first differences (linear interpolation)
In the chapter 11 of the Arithmetica logarithmica [10, pp. 21–24], Briggs considers the
subtabulation of logarithms, that is, the problem of finding logarithms between two values
of a table, or of finding to which number corresponds a logarithm which is between two
values in a table.
Subtabulation is an important means to compute new values of a table. For instance,
if we divide the interval [9123, 9124] in ten subintervals, we will find approximations of
the logarithms of 9123.1, 9123.2, etc., which do immediately provide approximations of
the logarithms of 91231, 91232, etc.
Briggs observes that the increments log(n + 1) − log n become smaller when n gets
larger, and that linear interpolation is more accurate
√ for large values of n. Briggs illustrates the use of linear interpolation to find a = 1200. He first finds A = log a =
1.539590 . . ., then B = 2 − A = 0.460409 . . .. If B = log b, then ab = 100. Briggs finds
c = 2886 such that C = log c = 3.46029 . . . has a decimal part slightly smaller than that
14
The original text reads Si Logarithmus Denominatoris auferatur è Logarithmo Numeratoris, restabit
Logarithmus Partium.
10
of B. Therefore log(ac) = log a + log c = 4.9998869497 . . . is slightly smaller than 5 and
ac is slightly smaller than 105 . Briggs finds h = 99973 such that log h is known and
h
≈ log(h + 1) − log h.
log h < log ac < log(h + 1). Finally, the interpolation gives log ac−log
ac−h
log ac−log h
Briggs obtains ac ≈ h + log(h+1)−log h = 99973.9726 . . . and then a ≈ 34.64101615 . . .
As can be seen, Briggs has transferred the linear interpolation to the end of his table,
where it is most accurate.
But Briggs’ process is tedious when c is large and not composed of small factors.
In order to simplify this process, Briggs constructed a table of numbers from 1024 to
9800, whose factors were only integers smaller than 10, together with their logarithms.
Briggs used this table in an example where he computed the square root of 10800 [10,
pp. 23–24]. He then needed to find a number whose logarithm had a decimal part close
to 0.98328812225653 and he took 9600 whose logarithm is 3.98227123303957. When it
comes to dividing by 9600, it is then much simpler than dividing by, say, 2886, which
contains the factor 37.
3.6.2
Subtabulation using second differences
The 12th chapter of the Arithmetica logarithmica [10, pp. 24–27] is devoted to subtabulation using second differences. In the first example, Briggs considers two numbers and
their logarithms and seeks to place nine equidistant numbers in between and to find their
logarithms. Briggs first considers the case where the second differences are almost equal.
In general, if ∆1 , ∆2 , ∆3 , etc., are the first, second, third, etc., differences of an
equidistant series of terms, an interpolation between the term A and the next one is
given by
zx = A + x∆1 + x ·
x−1 2
x−1 x−2 3
∆ +x·
·
∆ + ···
2
2
3
This is Newton’s forward difference formula, the differences ∆n being forward differences.15
If the second differences are constant, this expression reduces to z = A + x∆1 + x ·
x−1 2
1
2
∆ . We can take x = 0, 10
, 10
, . . . , 1, which gives:
2
z0.0 = A
z0.1 = A +
z0.3 = A +
z0.5 = A +
z0.7 = A +
z0.9 = A +
1 1
∆ −
10
3 1
∆ −
10
5 1
∆ −
10
7 1
∆ −
10
9 1
∆ −
10
9 2
∆
200
21 2
∆
200
25 2
∆
200
21 2
∆
200
18 2
∆
200
z0.2 = A +
z0.4 = A +
z0.6 = A +
z0.8 = A +
z1.0 = A +
We have the following differences:
15
Other interpolation formulæ use backward or central differences.
11
2 1
∆ −
10
4 1
∆ −
10
6 1
∆ −
10
8 1
∆ −
10
10 1
∆
10
16 2
∆
200
24 2
∆
200
24 2
∆
200
16 2
∆
200
z0.1 − z0.0 =
z0.3 − z0.2 =
z0.5 − z0.4 =
z0.7 − z0.6 =
z0.9 − z0.8 =
1 1
∆ −
10
1 1
∆ −
10
1 1
∆ −
10
1 1
∆ +
10
1 1
∆ +
10
45 2
∆
1000
25 2
∆
1000
5
∆2
1000
15 2
∆
1000
35 2
∆
1000
z0.2 − z0.1 =
z0.4 − z0.3 =
z0.6 − z0.5 =
z0.8 − z0.7 =
z1.0 − z0.9 =
1 1
∆ −
10
1 1
∆ −
10
1 1
∆ +
10
1 1
∆ +
10
1 1
∆ +
10
35 2
∆
1000
15 2
∆
1000
5
∆2
1000
25 2
∆
1000
45 2
∆
1000
This is exactly Briggs’ scheme, although he does not explain how he found it. His
first example is the interpolation between log 91235 and log 91236. The first and second
differences are ∆1 = 0.00000476014799 and ∆2 = −0.00000000005217 [10, p. 24]. Writing
in units of the 14th place, ∆1 = 476014799 and ∆2 = −5217. Briggs obtains:
1 1
∆
10
z0.1 − z0.0
z0.2 − z0.1
z0.3 − z0.2
z0.4 − z0.3
z0.5 − z0.4
z0.6 − z0.5
z0.7 − z0.6
z0.8 − z0.7
z0.9 − z0.8
z1.0 − z0.9
= 47601479.9
= 47601479.9 + 234.765 = 47601714.7
= 47601479.9 + 182.595 = 47601662.5
= 47601479.9 + 130.425 = 47601610.3
= 47601479.9 + 78.255 = 47601558.2
= 47601479.9 + 26.085 = 47601506.0
= 47601479.9 − 26.085 = 47601453.8
= 47601479.9 − 78.255 = 47601401.6
= 47601479.9 − 130.425 = 47601349.5
= 47601479.9 − 182.595 = 47601297.3
= 47601479.9 − 234.765 = 47601245.1
and from these differences, he obtains the values of zx for the nine intermediate values.
Briggs also gives a shortcut to compute directly a value such as z0.7 [10, pp. 25–26].
This shortcut uses a table of the cumulated factors of ∆2 . In this case,
105 2
1 1
∆ −
∆
10
1000
√
Briggs gives another√example where he seeks 147 [10, pp. 26–27]. From the logarithm
of 147, Briggs finds log 147 = 1.08365866737409. Using the table given in his chapter 11,
Briggs finds the nearest complement log 8192 = 0.91338994363175, the total of which is
0.99704861100584 (ignoring the integer part). He then finds two consecutive integers
whose logarithms have a decimal expansion which is approaching:
z0.7 = z0.0 + 7
log 99322 ≈ 4.99704545615255
log 99323 ≈ 4.99704982872152
12
By linear interpolation, Briggs finds that
log 99322.7 < 4.99704861100584 < log 99322.8
The interval obtained by linear interpolation will not always be correct, and presumably Briggs would have taken the next interval if the logarithm had lied outside of the
presumed interval.
In any case, using the interpolation with second differences, Briggs then computes
log 99322.7 and log 99322.8. Finally, Briggs uses another linear interpolation to interpolate between log 99322.7 and log 99322.8 and he finds 99322.721509238, the correct value (if the decimal part 4.99 . . . 584 were correct) being 99322.721509228879 . . ..
Dividing 99322.721509238 by 8192, Briggs finds 12.12435565298316, the correct value
(if the decimal part 4.99 . . . 584 were correct) being 12.12435565298204 and the exact
square root being 12.12435565298214. As a comparison, Briggs gives the true root as
12.124355652982141054.16
Briggs has used these methods to fill the blanks between 1 and 20000 and between
90001 and 100000.
3.6.3
Subtabulation by quinquisection
In the 13th chapter of the Arithmetica logarithmica [10, pp. 27–32], Briggs gives a new
method which is suitable for the interval 20000–90000. Briggs does not explain how he
obtained this method and we consider here a possible way of discovery.
Briggs had evidently been trying different approaches, using the differences in various
ways. His idea here is to compute the values of the logarithms from 5 to 5 using previously
computed logarithms. Then the values in between would be found by subtabulation. As
a start, we consider the logarithms from 20000 to 20005, given here to 22 places together
with their first differences:
∆1
n
log n
20000
4.3010299956639811952137
20001
4.3010517098452263503509
20002
4.3010734229408438648511
20003
4.3010951349509422879096
20004
4.3011168458756301524426
20005
4.3011385557150159750897
0.0000217141812451551372
0.0000217130956175145002
0.0000217120100984230585
0.0000217109246878645330
0.0000217098393858226471
Since the logarithms only increase slowly, the first differences are approximately equal
= 0.00002171201020 . . .. If only the values of log(5n) are known, this
to
approximation of the first differences can be used to find an approximation of log 20001,
but as it should be clear from the above values, the value of log 20001 will only be correct
to about eight places. Briggs, instead, wanted to have 14 decimal places.
log 20005−log 20000
5
16
There is actually a typographical error in the Arithmetica logarithmica, where the exact root is given
as 12.124355652982441054 [10, p. 27].
13
In order to obtain a more accurate interpolation, Briggs applies a correction to the
mean difference, as he did in chapter 12 using second differences. It is likely that Briggs
started with a range of logarithms, for instance one that he had computed using the
previous method. Here, we will consider that the values of log n are known for n = 20000,
20001, . . . Briggs could then put the first, second, third, . . . , differences in a table.
In order to simplify the exposition, we take the notations used by Legendre in 1815 [57].
y, y 0 , y 00 , etc., are the values of the logarithm for 20000, 20001, 20002, etc. The various
differences are δy, δy 0 , . . . , δ 2 y, . . .
20000 y = a
δy
20001 y 0
20002 y
00
20003 y
000
20004 y
iv
δy
0
δy 00
δy 000
2 0
δ y
2 00
δ y
2 000
δ y
20005 y = a
v
δ2y
0
δy iv
δ3y0
δ 3 y 00
δ 3 y 000
2 iv
δ y
δ4y
4 0
δ y
4 00
δ y
4 000
δ y
δ 3 y iv
δy v
20006 y
δ3y
2 v
δ y
δ5y
δ5y0
δ 5 y 00
δ 5 y 000
4 iv
δ y
δ3yv
.................................................
vi
20010 y x = a00
There are now basically two issues. First, given the values of a, a0 , a00 , . . . , Briggs must
have been looking for patterns to compute approximations of y 0 , y 00 , y 000 , y iv , . . . Second,
once Briggs had approximations of the δ i y j , he had to compute y j from them. These two
problems are of course related, and Briggs must have tried to express δa = a0 − a using
the subtabulated differences. We can for instance write:
δa = a0 − a = δy + δy 0 + δy 00 + δy 000 + δy iv
= (δy 00 − δ 2 y 0 − δ 2 y) + (δy 00 − δ 2 y 0 ) + δy 00 + (δy 00 − δ 2 y 00 ) + (δy 00 + δ 2 y 00 + δ 2 y 000 )
= 5δy 00 − 2δ 2 y 0 − δ 2 y + 2δ 2 y 00 + δ 2 y 000
= 5δy 00 − 2δ 2 y 0 − (δ 2 y 0 − δ 3 y) + 2(δ 2 y 0 + δ 3 y 0 ) + (δ 2 y 00 + δ 3 y 00 )
= 5δy 00 − δ 2 y 0 + δ 3 y + 2δ 3 y 0 + δ 3 y 00 + δ 2 y 00
= 5δy 00 − δ 2 y 0 + (δ 3 y 0 − δ 4 y) + 2δ 3 y 0 + δ 3 y 00 + δ 2 y 00
= 5δy 00 − δ 2 y 0 + 3δ 3 y 0 − δ 4 y + δ 3 y 00 + δ 2 y 00
= 5δy 00 − δ 2 y 0 + 3δ 3 y 0 − (δ 4 y 0 − δ 5 y) + (δ 3 y 0 + δ 4 y 0 ) + δ 2 y 00
= 5δy 00 − δ 2 y 0 + 4δ 3 y 0 + δ 5 y + δ 2 y 00
= 5δy 00 + (δ 2 y 00 − δ 2 y 0 ) + 4δ 3 y 0 + δ 5 y
= 5δy 00 + 5δ 3 y 0 + δ 5 y
So, we have the simple expression
δ5y
δa
= δy 00 + δ 3 y 0 +
5
5
14
(2)
There are of course much quicker ways to derive this equation [57, 40], but Briggs
certainly found it after painstaking effort. The right-hand side of the equation uses
the mean first
differences which are positioned midway from a and a0 . Briggs calls δa
5
difference.
20000 y = a
δy
20001 y 0
δ2y
0
δy
δ3y
00
2 0
20002 y
δ y
δ4y
00
3 0
δy
δ y
δ5y
000
2 00
4 0
20003 y
δ y
δ y
δy 000
δ 3 y 00
20004 y iv
δ 2 y 000
iv
δy
20005 y v = a0
Already before finding this formula, Briggs must have known that δy ≈ δy 0 ≈ δy 00 · · · ≈
equation shows that δa
can be obtained from δy 00 using a small correction
5
In fact, looking at the first differences was probably enough for Briggs to
notice that δa
was closest to δy 00 . For instance, if a = log 20000, we have, as seen above,
5
δa
but this
5
5
3 0
δ y + δ 5y .
δa
5
δy
δy 0
δy 00
δy 000
= 0.0000217120102 . . .
= 0.0000217141812 . . .
= 0.0000217130956 . . .
= 0.0000217120100 . . .
= 0.0000217109246 . . .
So δy 00 can also be obtained from δa
using the correction −δ 3 y 0 − 15 δ 5 y.
5
2
After that, Briggs must have noticed that δ 2 y ≈ δ 2 y 0 ≈ δ25a , and more exactly
δ 2 y iv .
Probably after a long search, Briggs came up with
δ2 a
25
≈
7
2
1
δ2a
= δ 2 y iv + 2δ 4 y 000 + δ 6 y 00 + δ 8 y 0 + δ 10 y
(3)
25
5
5
25
This formula also uses differences which are symmetrically located between a and a00 .
The next equation is
δ3a
= δ 3 y vi + 3δ 5 y v + · · ·
(4)
125
and Briggs found a general way to obtain these formulæ without having to go through
a long algebraic manipulation. The coefficients of these equations are given by Briggs in
his Arithmetica logarithmica [10, p. 29].
In order to use these equations, we can see that the differences decrease quickly and
become neglectible at some point. Neglecting all differences of order greater than 5 results
in the following simplified equations:
δa
δ5y
= δy 00 + δ 3 y 0 +
5
5
δ4a
= δ 4 y viii
625
δ2a
= δ 2 y iv + 2δ 4 y 000
25
δ5a
= δ5yx
55
15
δ3a
= δ 3 y vi + 3δ 5 y v
125
The last two equations give us a means to compute δ 5 y (or δ 5 y v , δ 5 y x , etc.) and δ 4 y 000
δ3 a
(or δ 4 y viii , etc.). Using the equation for 125
, we can compute δ 3 y vi (or δ 3 y 0 ), and using
2
the equation for δ25a , we can compute δ 2 y iv . Finally, the first equation gives δy 00 .
The following table shows in boxes the values that have been approximated. The
pattern of boxes is repeated every five values.
20000 y = a
δy
20001 y 0
20002 y
00
20003 y
000
20004 y
iv
δy
0
δy 00
δy 000
2 0
δ y
2 00
δ y
2 000
δ y
20005 y = a
v
δ2y
0
δy iv
20010 y = a
x
4 000
δ y
δ5yv
4 vi
δ y
δ y
δ 3 y vii
2 viii
δ 5 y vi
4 vii
δ y
δ y
δ 3 y viii
2 ix
δ y
δ 5 y 000
δ 5 y iv
δ 3 y vi
δy ix
δ 5 y 00
4 v
2 vii
00
δ y
δ5y0
δ y
δ y
ix
4 00
δ3yv
2 vi
viii
δ y
δ5y
4 iv
δ y
vii
4 0
δ y
2 v
vi
δy viii
20009 y
δ 3 y 000
δ4y
δ 3 y iv
δy vii
20008 y
δ 3 y 00
δ y
δy vi
20007 y
δ3y0
2 iv
δy v
20006 y
δ3y
δ 5 y vii
4 viii
δ y
......................................................
All that now remains to do is to compute the other differences δy, δy 0 , δy 000 , and δy iv .
Assuming δ 5 y = δ 5 y 0 = δ 5 y 00 , we compute δ 4 y 00 , δ 4 y 0 , and δ 4 y. All the other values follow,
until the first differences, and finally the logarithms themselves: y 0 = a+δy, y 00 = y 0 +δy 0 ,
etc.
This method, Briggs’ quinquisection, was reused in the Trigonometria britannica [11].
3.6.4
The method of quinquisection and Newton’s interpolation
As could be expected, Briggs’ method of quinquisection and Newton’s forward difference
formula agree. Briggs’ quinquisection is actually a special case of Newton’s formula seen
from a different vantage point. In this section, we only give some hints for the comparison,
but we do not give a complete proof.17
In order to compare the two methods, we can rewrite the method of quinquisection using only the differences involved in Newton’s formula. We will only sketch the derivation,
5
−δ 3 y 0 − δ 5y ,
but the details can easily be filled. We have seen above that we have δy 00 = δa
5
17
For details on Newton’s work on interpolation and subtabulation by finite differences, see Whiteside [114], [115, pp. 672–681]. Newton was apparently unaware of Briggs’ work on finite differences and
subtabulation [112, pp. 13–14], [113, p. 234], [114, pp. 3–5].
16
but it is better to start with δy xii , in order to avoid indices before a. By an easy transformation, we obtain
1
1
14
δy xii = δa00 − 3 δ 3 a0 + 6 δ 5 a
5
5
5
Next, we consider the following equations:
δy xi
δ2yx
δ 3 y ix
δ 4 y ix
= δy xii − δ 2 y xi
= δ 2 y ix + δ 3 y ix
= δ 3 y x − δ 4 y ix
= δ 4 y viii + δ 5 y viii
= δy xi − δ 2 y x
= δ2yx + δ3yx
= δ 3 y xi − δ 4 y x
= δ 4 y ix + δ 5 y ix
δy x
δ 2 y xi
δ3yx
δ4yx
We keep only the terms of order 4 or lower and obtain
1 4
δ a + ···
54
1
δ4yx = 4 δ4a + · · ·
5
1
1
3 x
δ y = 3 δ 3 a0 − 4 δ 4 a + · · ·
5
5
1 3 0
2
3 ix
δ y = 3 δ a − 4 δ4a + · · ·
5
5
1 2 0
1
4
δ a + 3 δ 3 a0 − 4 δ 4 a + · · ·
2
5
5
5
1 2 0
2 3 0
1
2 xi
δ y = 2 δ a + 3 δ a − 3 δ4a + · · ·
5
5
5
1 00
1 2 0
3 3 0
1
xi
δy = δa − 2 δ a − 3 δ a + 3 δ 4 a + · · ·
5
5
5
5
1 00
2 2 0
4 3 0
9
x
δy = δa − 2 δ a − 3 δ a + 4 δ 4 a + · · ·
5
5
5
5
δ 4 y ix =
δ2yx =
We then introduce δ 2 a00 using δ 2 a0 = δ 2 a00 − δ 3 a0 and make similar other replacements,
leading to
2
6
21
1
δy x = δa00 − 2 δ 2 a00 + 3 δ 3 a00 − 4 δ 4 a00 + · · ·
5
5
5
5
This formula contains explicitely all terms of orders up to the fourth. We can compare
these first four terms with those of Newton’s forward difference formula. We have
1
1
δy x = δa00 + ·
5
5
1
5
− 1 2 00 1
δ a + ·
2
5
1
5
−1
·
2
1
5
− 2 3 00 1
δ a + ·
3
5
1
5
−1
·
2
1
5
−2
·
3
1
5
− 3 4 00
δ a + ···
4
The first value obtained by quinquisection therefore agrees to our level of accuracy
with the value that would have been obtained by Newton’s interpolation formula. The
same applies to δy xi , δy xii , etc.
3.6.5
Link with Bürgi’s interpolation
Together with the publication of Jost Bürgi’s “Coss,” List and Bialas have suggested that
Bürgi may have used for the computation of his Canon sinuum an interpolation scheme
identical or similar to Briggs’ quinquisection [58, pp. 76–77, 100, 116–123]. Briggs had
also used his quinquisection when he computed sines in the Trigonometria britannica.
Bürgi, however, kept the details of his interpolation scheme somewhat secret, and we
know little more than that it was based on differences. It would be preposterous to
suggest that Briggs was inspired by Bürgi, perhaps through Ursus, as we have shown
that Briggs could very well arrive to his scheme independently.
17
Although Bürgi considers interpolating one-degree intervals by steps of 200 or 400 [58,
pp. 76–77], that is dividing in 1800 or 900 smaller intervals, Oechslin suggested an interpretation of Bürgi’s description in the case of quinquisection [75, pp. 81–92]. Considering
again the following table
y=a
δy
y0
y
00
y
000
y
iv
δy
0
δy
00
δ3y
2 0
δ y
3 0
δ y
2 00
δy 000
δ y
δ 3 y 00
2 000
δ y
y =a
v
δ2y
δ 3 y 000
δy iv
0
2 iv
δ y
4 0
δ y
4 00
δ y
4 000
δ y
δ 3 y iv
δy v
y
δ4y
2 v
δ5y
δ5y0
δ 5 y 00
δ 5 y 000
4 iv
δ y
δ y
δ3yv
.........................................
vi
y x = a00
we can transform it into
y=a
5δy
y0
y 00
y
000
y
iv
5δy
0
5δy
00
y =a
52 δ 2 y 0
2 2 00
5δy 000
v
52 δ 2 y
5δ y
2 2 000
5δ y
0
5δy iv
3 3 0
5δ y
53 δ 3 y 00
53 δ 3 y 000
2 2 iv
5δ y
5δy
y vi
53 δ 3 y
54 δ 4 y
4 4 0
5δ y
4 4 00
5δ y
4 4 000
5δ y
3 3 iv
5δ y
v
52 δ 2 y v
55 δ 5 y
55 δ 5 y 0
55 δ 5 y 00
55 δ 5 y 000
54 δ 4 y iv
3 3 v
5δ y
..................................................
y x = a00
Oechslin (who does not mention Briggs) wants to interpolate between a and a0 . So,
he will compute five values for the first differences, between a and a0 . The third of these
five values is δa. All these values will be divided by 5 and then added to one another
to produce y 0 , y 00 , etc. Oechslin’s five values are therefore approximations of 5δy, 5δy 0 ,
etc. But in order to obtain these approximations, Oechslin needs approximations of their
differences, that is approximations of 5δ 2 y, 5δ 2 y 0 , etc. He in fact obtains approximations
of 52 δ 2 y, 52 δ 2 y 0 , etc., which he then divides by 5. Eventually, and to start with, Oechslin
needs approximations of the last differences, which are here 55 δ 5 y, 55 δ 5 y 0 , etc. But, as
shown above, an approximation of 55 δ 5 y, 55 δ 5 y 0 , etc., is δ 5 a. An approximation of 54 δ 4 y,
18
54 δ 4 y 0 , etc., is δ 4 a. An approximation of 53 δ 3 y, 53 δ 3 y 0 , etc., is δ 3 a. An approximation of
52 δ 2 y, 52 δ 2 y 0 , etc., is δ 2 a. And an approximation of 5δy, 5δy 0 , etc., is δa.
In order to increase the accuracy, we can take
55 δ 5 y x
54 δ 4 y viii
53 δ 3 y vi
52 δ 2 y iv
5δy 00
≈ δ5a
≈ δ4a
≈ δ3a
≈ δ2a
≈ δa
and then write
δ5a
5
5
δ
a
54 δ 4 y 00 ≈ 54 δ 4 y 0 +
5
......
54 δ 4 y
53 δ 3 y 0 ≈ 53 δ 3 y +
5
4 4 0
5δ y
53 δ 3 y 00 ≈ 53 δ 3 y 0 +
5
......
54 δ 4 y 0 ≈ 54 δ 4 y +
If we apply this interpolation to a table of sines for each degree between 0◦ and 10◦ ,
with five differences and 10 decimal places, we obtain the intermediate values with only
five or six exact places. If instead we apply the interpolation to a table of sines for all
minutes from 00 to 100 , we obtain eight to nine exact decimal places.
Oechslin’s scheme is actually not as accurate as Briggs’, although they may look
similar. In order to compare the two schemes, let us take a simpler case with only three
differences. Such an example is given by Oechslin [75, pp. 83].
y=a
y0
y
00
y
000
y
iv
δ3a
α4
α5
y =a
v
y
y
y
viii
y
0
δa0
y =a
x
δ3a
δ a
α2
δ3a
α6
α7
α8
α3
ix
δ3a
2
α1
vi
vii
δ3a
δa
δ3a
δ3a
δ3a
δ3a
00
19
In Oechslin’s example, δ 3 a is constant. Consider now the values of y vi , y vii , y viii , and
y ix . We have
α4 + α5 + δ 2 a
5
α8
= δa0 +
5
3
δ
a
= δ2a −
5
δ3a
= δ2a + 2
5
α1
v
=y +
5
δa0
= y vii +
5
α4 + α5 + δ 2 a + α6
5
3
δ a
= δ2a − 2
5
3
δ
a
= δ2a +
5
δ3a
= δ2a + 3
5
α2
vi
=y +
5
α3
= y viiii +
5
α1 = δa +
α2 = δa +
α3
α4
α5
α7
y vi
y viii
α6
α8
y vii
y ix
therefore
δa
3
3 3
+ δ2a −
δ a
5
25
125
δa
7
5 3
y vii = a0 + 2 + δ 2 a −
δ a
5
25
125
δa δa0
7
5 3
y viii = a0 + 2 +
+ δ2a −
δ a
5
5
25
125
δa0
8
2 3
δa
+ δ2a −
δ a
y ix = a0 + 2 + 2
5
5
25
125
δa
δa0 11 2
5 3
(y x ) = a0 + 2 + 3
+ δ a−
δ a
5
5
25
125
y vi = a0 +
The last value is the one that we would obtain by a further step, but normally we use
the value a00 .
We can compare these equations with those obtained by Briggs in the same conditions.
Assuming δ 4 a = 0, we find
δa
= δy 00 + δ 3 y 0
5
δ2a
= δ 2 y iv
25
δ3a
= δ 3 y vi
125
20
and
δ 2 y 000 = δ 2 y iv − δ 3 y
δ 2 y 00 = δ 2 y 000 − δ 3 y
δa
− δ 3 y + (δ 2 y 000 − δ 3 y) + (δ 2 y iv − δ 3 y) + δ 2 y iv
5
δa
δa
=
− 3δ 3 y + 2δ 2 y iv + δ 2 y 000 =
− 4δ 3 y + 3δ 2 y iv
5
5
δa
y vi = a0 + δy v = a0 +
+ 3δ 2 y iv − 4δ 3 y
5
3
4 3
δa
+ δ2a −
δ a
= a0 +
5
25
125
7
7 3
δa
δ a
y vii = a0 + 2 + δ 2 a −
5
25
125
δa δa0
7
8 3
viii
0
y =a +2 +
+ δ2a −
δ a
5
5
25
125
δa
6 3
δa0
8
y ix = a0 + 2 + 2
+ δ2a −
δ a
5
5
25
125
δa
δa0 10 2
(y x ) = a0 + 2 + 3
+ δ a
5
5
25
Oechslin’s formulæ slightly differ from these ones. In this case, Briggs’ formulæ give
the exact values, and Oechslin’s scheme is therefore only an approximation. For instance,
if we apply Briggs’ scheme to Oechslin’s example where he interpolates a function such
that a = 10, a0 = 20, a0 = 40, δa = 10, δa0 = 20, δ 2 a = 10, δ 3 a = 5, the formulæ above
give exactly Oechslin’s values, and in particular the interpolated value of y x is 40.2 [75,
pp. 83]. But Briggs’ scheme gives the correct value 40.
Oechslin’s interpretation applied to larger intervals is not more satisfactorily, and it
seems doubtful that this was Bürgi’s scheme, as Bürgi would certainly have noticed a
difference between his tables and previous sine tables.
In fact, Bürgi’s description does not seem to allude to quinquisection, and we may have
to look for another idea, as was suggested in our study of Bürgi’s progression tables [88].
δy v = δy 00 + δ 2 y 00 + δ 2 y 000 + δ 2 y iv =
3.7
The radix method
In Chapter 14 of the Arithmetica logarithmica [10, pp. 33–36], Briggs gives the so-called
radix method, for finding the logarithm of a number.18 This method involves the use
of radices, or numbers of the form 1 + 10rn , together with their logarithms. There are
several variants of this method. A number N is for instance decomposed in a product
N0 (1 + q1 )(1 + q2 ) . . ., where log N0 is known and the qi are fractions r · 10−n found in
an iterative way. The value of log N is then obtained by a mere addition using the radix
table. Historical descriptions of the writings on the radix method were published by
Ellis [23, 24] and Lupton [59, 60] and further analyses are given by Glaisher [38].
In his first example, Briggs considers the number x = 3.66067578833852 and shows
how to compute the number of which it is the logarithm, that ism its antilogarithm. From
18
Given that Vlacq omitted Briggs’ chapters 12 and 13, the radix method appears in Chapter 12 of
Vlacq’s Arithmetica logarithmica [105].
21
x, Briggs subtracts 3, then log 3 = 0.477121254719662, log 1.4 = 0.146128035678238, and
log 1.09 = 0.037426497940624 and finds nearly 0, so that x ≈ 3 + log 3 + log 1.4 + log 1.09.
All these logarithms are found in the radix table given by Briggs [10, p. 32]. It should be
noted that Briggs did not subtract log 1.5, although x − 3 − log 3 > log 1.5, so that this
method can obviously be applied in different ways. In any case, Briggs concludes that
x = log(103 · 3 · 1.4 · 1.09) = log 4578. In a second example, Briggs suggests to first take
the nearest smaller logarithm in the main table (1–20000, 90001–100000), to subtract it
from the given number x and to continue with the radix table.
The same radix table can be used to find the logarithm of any number. Briggs
considers the problem of finding the logarithm of x = 3041.851528656. In order to express
Briggs’s method, we first define ν(x) to be the truncation of x to one significant digit.19
For instance, ν(0.0002800160 . . .) = 0.0002. The method then consists in first dividing
this number by x0 = 3041, whose logarithm lies in the maintable.20 Then the following
r1
, r2 = x − x0 (1 + q1 ),
sequence is constructed: r1 = x − x0 = 0.851528656, q1 = ν x−r
1
r2
r3
q2 = ν x−r
, r3 = x−x0 (1+q1 )(1+q2 ), q3 = ν x−r
, r4 = x−x0 (1+q1 )(1+q2 )(1+q3 ),
2
3
r4
q4 = ν x−r
, r5 = x − x0 (1 + q1 )(1 + q2 )(1 + q3 )(1 + q4 ), . . .
4
With this procedure, x is approximated by x0 (1 + q1 )(1 + q2 )(1 + q3 )(1 + q4 ) and
therefore log x = log x0 + log(1 + q1 ) + log(1 + q2 ) + · · · , all of these logarithms being
known. In the case of the above example, Briggs found 3041.851528656 = 3041 · 1.0002 ·
1.00008 · · · and therefore log 3041.851528656 = log 3041 + log 1.0002 + log 1.00008 + · · · .
In fact, since Briggs chose 3041.851528656 = 3041 · 1.0002 · 1.00008, we have exactly
log 3041.851528656 = log 3041 + log 1.0002 + log 1.00008. Briggs gives a second example
following the same principle, with x = 2966.82051456 and finds q1 = 0.0002, q2 = 0.00007,
q3 = 0.000006, etc., and eventually log 2966.82051456 = 3.472291273349534, the correct
value being 3.472291273349533 . . ..
The radix method is fairly straightforward for a manual application, the most difficult
ri
. In the Arithmetica logarithmica, Briggs
part being the computation of the ratios x−r
i
organized the computations in such a way that one presumes they could be taught easily
using standard forms.
According to Glaisher [38], this method was first applied in 1618 in an anonymous
appendix to the second edition of Wright’s translation of Napier’s Descriptio [69]. By
an analysis of the notations, Glaisher has concluded that the author was in fact William
Oughtred.
4
The computers
Briggs was aided by other computers for which he prepared forms that they could fill [96,
p. 51]. We do unfortunately not know the names of those who assisted Briggs, except in
a few instances. Edmund Gunter, who published the first decimal logarithms of trigonometric functions [41], may have been one of them [36, p. 381]. There also remains a letter
from J. Wells to Briggs, dated January 9, 1621, from which it appears that Wells assisted
x
E(log x)
We could express ν(x) formally as ν(x) = E 10E(log
where E(x) is the greatest integer
x) × 10
smaller than x.
20
If Briggs’ main table had been complete, he would certainly have divided x by 30418.
19
22
Briggs in the computations of the logarithms [80, vol. 1, pp. 5–6], [36, p. 381]. Wells was
the later author of a Sciographia in 1635 [108].
There is also Euclid Speidell’s testimony [98] (cited by Egen [21, p. 257]), according
to which Briggs was assisted by eight computers for one year. This does not totally fit
with the time elapsed between publications, but it gives nevertheless a general idea of
how the calculations were performed.
5
Vlacq’s table and Briggs’ projects
In 1628, Adriaan Vlacq published a table giving the logarithms of the numbers from 1 to
100000 with only 10 places, which he called a second edition of Briggs’ table, although it
actually wasn’t [105].
Glaisher [36, pp. 380–381] cites an excerpt from a letter dated October 25th, 1628
from Briggs to Pell in which Briggs mentions his projects and how they were altered by
Vlacq:21
My desire was to have those Chiliades that are wantinge betwixt 20 and 90 calculated and printed, and I had done them all almost by my selfe, and by some
frendes whom my rules had sufficiently informed, and by agreement the business was conveniently parted amongst us; but I am eased of that charge and
care by one Adrian Vlacque, an Hollander, who hathe done all the whole hundred chiliades and printed them in Latin, Dutche, and Frenche, 1000 bookes
in these 3 languages, and hathe sould them almost all. But he hathe cutt of 4
of my figures throughout; and hathe left out my Dedication, and to the reader,
and two chapters the 12 and 13, in the rest he hathe not varied from me at
all.
It is likely that Briggs had planned to fill the missing interval with 14 places, and
even that this project had reached an advanced stage, but that Vlacq’s publication cut
his project short [4, p. 220]. According to Glaisher, there is no doubt that Briggs’ friends
were annoyed at Vlacq’s publication of 1628 [35, p. 301]. And indeed, in 1631, Richard
Norwood wrote, referring to Miller’s 1631 edition of Vlacq’s tables:
And here I have just occasion to blame the ill dealings of these men, not
only towards my selfe, as I have before noted in the Preface to the Reader,
but likewise towards Mr. Briggs, both in the matter before mentioned, and in
printing a second edition of his Arithmetica Logarithmica in Latine, whilest
he lived, against his minde and liking: and brought them over to sell, when the
first were unsolde; so frustrating those additions which Mr. Briggs intended
in his second Edition, and moreover leaving out some things, that were in
the first edition, of special moment. A practice of very ill consequence, and
tending to the great discouragement of such as take paines in this kind.22
21
22
The full letter is reproduced in Halliwell’s Rara mathematica [44, pp. 55–57].
[74], cited in [67, p. 172]
23
According to Hallowes, Briggs must then have felt that he could not complete both the
tables of the logarithms of numbers and the logarithms of trigonometric functions, that
the completion of the Arithmetica logarithmica had been reduced to a certain routine,
and he must then have turned to the trigonometric functions exclusively [45, p. 85].
6
Briggs’ and Vlacq’s legacy
Briggs’ table served as a basis for Vlacq’s own Arithmetica logarithmica, and therefore is
the foundation of almost all later extensive tables of logarithms until the 20th century.
For 300 years, Briggs’ scheme lay uncompleted. There have been several undertakings,
but none that would carry out completely Briggs’ scheme was ever printed before 1952.
The most famous of them, the Tables du cadastre, only guaranteed 12 places23 and did
not go beyond Briggs’ 14 places [35, p. 301]. Edward Sang’s tables were most extensive,
but were never printed [18].
Edward Sang was one of the few to be critical towards the usefulness of the Tables du
cadastre for checking the tables of Briggs or Vlacq [91]. Obviously, if 12 decimal places
are exact (in the above sense) in the Tables du cadastre, this means that the error on
the unrounded logarithm is less than 5 · 10−13 . The 13th and 14th decimals are therefore
uncertain and the values of the Tables du cadastre cannot be used reliably (except in
certain cases) to check these decimals in other tables with certainty.
Eventually, in 1924, the tercentenary of Briggs’ table was celebrated by starting
the publication of Thompson’s Logarithmetica Britannica [100], which was completed
in 1952 [101]. Thompson’s table gave the logarithms of all integers up to 100000 with 20
decimal places.
7
The tables’ errors
Briggs’ table contains a number of errors and an errata is given at the beginning of
the Arithmetica logarithmica. A supplementary errata was given by Lefort in 1858 [55,
p. 147]. A comparison of Briggs’ table with Prony’s Tables du cadastre was made around
1800 by Letellier and Guyetant, two employees of the French cadastre, and their result
was added at the end of Briggs’ somewhat incomplete volume at the Bibliothèque SainteGeneviève in Paris.24 They compared the 13th and 14th decimals of Briggs’ table with
those of the Tables du cadastre, and since the Tables du cadastre are only guaranteed
to give 12 exact decimals,25 only large errors in Briggs’ table could be found this way.
The errata which was therefore gathered was restricted to errors occuring before the 12th
decimal for n > 10000. For n < 10000, the Tables du cadastre contain more accurate
values of the logarithms and the errata sometimes gives errors beyond the 11th decimal.
Here and in the sequel, it should be understood that we mean that the error is smaller than 5 · 10−13 ,
which in fact does not guarantee the first 12 decimal places.
24
Bibliothèque Sainte-Geneviève, FOL V 64(2) INV 84 RES. Prony has apparently added the same
errata to his own copy of the Arithmetica Logarithmica [56, p. 996], which he bought in Montpellier.
(minutes of the Bureau des longitudes, 8 frimaire 11, where Prony announced his errata [28])
25
More exactly, the error on the 12th decimal of the unrounded logarithm is smaller than half a unit
of the 13th place.
23
24
The comparison could have been done systematically until the 14th place in this interval,
but it was apparently not done.26 In any case, it is known that there are a large number
of small errors in Briggs’ table.27
A more comprehensive errata was given in 1952 by Thompson in his Logarithmetica
Britannica [101, pp. lxxviii–lxxxiii]. An overview of the erratas is given by Fletcher
et al. [30, p. 794]. Thompson found almost 1200 errors, ignoring errors of one unit in the
fourteenth decimal, and the number of errors affecting the first twelve decimals appears
to be over 180.
8
Structure of the tables and recomputation
The original Arithmetica logarithmica contains an introduction of 88 pages, immediately
followed by the first page of the tables, giving the logarithms of all integers from 1 to 20000
and from 90001 to 100000 to 14 decimal places. These tables were recomputed using the
GNU mpfr multiple-precision floating-point library developed at INRIA [31], and give
the exact values. The comparison of our table and Briggs’ will therefore immediately
show where Briggs’ table contains errors, and this is of course one of the purposes of
this reconstruction. Apart from the change in accuracy, we have tried to be as faithful
as possible to the original tables. We have however added some values in a few cases
where Briggs had left blanks. The original tables had for instance a blank space for the
difference between log 2 and log 1 and we have put the correct value.
In addition to the reconstruction of Briggs’ Arithmetica logarithmica, we have also
reconstructed the “ideal” Arithmetica logarithmica, that is, a table giving the logarithms
for the whole range from 1 to 100000, as Briggs had wanted it. This reconstruction is
given in a separate document [87].
9
Acknowledgements
It is a pleasure to thank Ian Bruce who, by providing translations of key parts of Briggs’
Arithmetica logarithmica and Trigonometria britannica, made the present analysis much
easier.
26
The logarithms below 10000 in the Tables du cadastre do not contain added figures for comparison,
which seems to hint to the fact that no comparison was made. Moreover Lefort also seems to regret this
omission [55, p. 147]. On the other hand, as shown in our study of the Tables du cadastre [90], these
logarithms were computed to 19 decimals, but their accuracy was not 19 decimals. It should also be
noted that as a consequence of this comparison and of the trust Prony had in his tables, he mistakenly
attributed some errors to Briggs, when the errors were in fact in Prony’s tables [90].
27
In 1910, before the publication of his own tables, Henri Andoyer wrote that the last place of Briggs’
tables was usually wrong by several units [3].
25
References
The following list covers the most important references28 related to Briggs’ tables. Not
all items of this list are mentioned in the text, and the sources which have not been seen
are marked so. We have added notes about the contents of the articles in certain cases.
[1] Juan Abellan. Henry Briggs. Gaceta Matemática, 4 (1st series):39–41, 1952. [This
article contains many incorrect statements.]
[2] Ian R. Adamson. The administration of Gresham College and its fluctuating
fortunes as a scientific institution in the seventeenth century. History of
Education, 9(1):13–25, March 1980.
[3] Marie Henri Andoyer. Nouvelles Tables trigonométriques fondamentales. Comptes
rendus hebdomadaires des séances de l’Académie des sciences, 150:591–592,
janvier-juin 1910.
[4] Anonymous. Contributions to scientific biography. The Edinburgh journal of
science, 5:219–222, 1831.
[5] Évelyne Barbin et al., editors. Histoires de logarithmes. Paris: Ellipses, 2006.
[6] Peter Barlow. A new mathematical and philosophical dictionary; etc. London:
Whittingham and Rowland, 1814.
[7] Janet Beery and Jacqueline Stedall, editors. Thomas Harriot’s doctrine of
triangular numbers: the ‘Magisteria magna’. Zürich: European Mathematical
Society, 2009.
[8] H. S. Bennett. English books and readers, III: 1603–1640. Cambridge: Cambridge
University Press, 1970.
[9] Henry Briggs. Logarithmorum chilias prima. London, 1617. [The tables were
reconstructed by D. Roegel in 2010. [82]]
[10] Henry Briggs. Arithmetica logarithmica. London: William Jones, 1624. [An English
translation of the introduction was made by Ian Bruce and can be found on the web.]
[11] Henry Briggs and Henry Gellibrand. Trigonometria Britannica. Gouda: Pieter
Rammazeyn, 1633. [The tables were reconstructed by D. Roegel in 2010. [85]]
[12] Ian Bruce. The agony and the ecstasy — the development of logarithms by Henry
Briggs. The Mathematical Gazette, 86(506):216–227, July 2002.
28
Note on the titles of the works: Original titles come with many idiosyncrasies and features (line
splitting, size, fonts, etc.) which can often not be reproduced in a list of references. It has therefore
seemed pointless to capitalize works according to conventions which not only have no relation with the
original work, but also do not restore the title entirely. In the following list of references, most title
words (except in German) will therefore be left uncapitalized. The names of the authors have also been
homogenized and initials expanded, as much as possible.
The reader should keep in mind that this list is not meant as a facsimile of the original works. The
original style information could no doubt have been added as a note, but we have not done it here.
26
[13] Evert Marie Bruins. On the history of logarithms: Bürgi, Napier, Briggs, De
Decker, Vlacq, Huygens. Janus, 67(4):241–260, 1980.
[14] Florian Cajori. A history of mathematics. New York: Macmillan and co., 1894.
[15] Moritz Cantor. Vorlesungen über Geschichte der Mathematik. Leipzig:
B. G. Teubner, 1900. [volume 2, pp. 737–739, 743–748 on Briggs]
[16] Julian Lowell Coolidge. The story of the binomial theorem. The American
Mathematical Monthly, 56(3):147–157, March 1949.
[17] Lesley B. Cormack. Charting an empire. Chicago: University of Chicago Press,
1997.
[18] Alex D. D. Craik. The logarithmic tables of Edward Sang and his daughters.
Historia Mathematica, 30(1):47–84, February 2003.
[19] Jean-Baptiste Joseph Delambre. Histoire de l’astronomie du moyen âge. Paris:
Veuve Courcier, 1819.
[20] Jean-Baptiste Joseph Delambre. Histoire de l’astronomie moderne. Paris: Veuve
Courcier, 1821. [two volumes, volume 1, pp. 532–545 and volume 2, pp. 76–88 on Briggs]
[21] Peter Nikolaus Caspar Egen. Handbuch der allgemeinen Arithmetik, volume 1.
Berlin: Duncker und Humblot, 1833.
[22] Alexander J. Ellis. On an improved bimodular method of computing natural and
tabular logarithms and anti-logarithms to twelve or sixteen places, with very brief
tables. Proceedings of the Royal Society of London, 31:381–398, 1881.
[23] Alexander J. Ellis. On the potential radix as a means of calculating logarithms to
any required number of decimal places, with a summary of all preceding methods
chronologically arranged. Proceedings of the Royal Society of London, 31:398–413,
1881.
[24] Alexander J. Ellis. Postscript to the chronological summary of methods of
computing logarithms in my paper on the potential radix. Proceedings of the
Royal Society of London, 32:377–379, 1881.
[25] Jean-Marie Farey et Patrick Perrin. Les logarithmes de Briggs (1624). In La
mémoire des nombres, pages 319–341. IREM de Basse Normandie, 1997. [The same
article was also published separately in 1995 [26].]
[26] Jean-Marie Farey and Patrick Perrin. Les logarithmes de Briggs. Repères-IREM,
21:61–77, October 1995. [This is a separate publication of [25].]
[27] Mordechai Feingold. The mathematicians’ apprenticeship: science, universities
and society in England, 1560–1640. Cambridge: Cambridge University Press,
1984.
27
[28] Jean-Marie Feurtet. Procès-verbaux du Bureau des longitudes (juillet 1795–mai
1804) : le Bureau des longitudes (1795–1854) : De Lalande à Le Verrier. thèse
pour le diplôme d’archiviste paléographe, Ecole nationale des Chartes, 2005.
[29] Alan Fletcher. Early logarithmic works. Nature, 148(3763):728, 1941.
[30] Alan Fletcher, Jeffery Charles Percy Miller, Louis Rosenhead, and Leslie John
Comrie. An index of mathematical tables. Oxford: Blackwell scientific
publications Ltd., 1962. [2nd edition (1st in 1946), 2 volumes]
[31] Laurent Fousse, Guillaume Hanrot, Vincent Lefèvre, Patrick Pélissier, and Paul
Zimmermann. MPFR: A multiple-precision binary floating-point library with
correct rounding. ACM Transactions on Mathematical Software, 33(2), 2007.
[32] Jean-Pierre Friedelmeyer. L’invention des logarithmes par Neper et le calcul des
logarithmes décimaux par Briggs. Activités mathématiques et scientifiques,
61:105–122, February 2007.
[33] David Gibb. A course in interpolation and numerical integration for the
mathematical laboratory, volume 2 of Edinburgh Mathematical Tracts. London:
G. Bell & sons, Ltd., 1915.
[34] George Alexander Gibson. Napier’s logarithms and the change to Briggs’s
logarithms. In Knott [54], pages 111–137.
[35] James Whitbread Lee Glaisher. Notice respecting some new facts in the early
history of logarithmic tables. The London, Edinburgh and Dublin Philosophical
Magazine and Journal of Science, Series 4, 44:291–303, 1872.
[36] James Whitbread Lee Glaisher. On early logarithmic tables, and their calculators.
The London, Edinburgh and Dublin Philosophical Magazine and Journal of
Science, Series 4, 45(301):376–382, May 1873.
[37] James Whitbread Lee Glaisher. Report of the committee on mathematical tables.
London: Taylor and Francis, 1873. [Also published as part of the “Report of the forty-third
meeting of the British Association for the advancement of science,” London: John Murray, 1874.]
[38] James Whitbread Lee Glaisher. The earliest use of the radix method for
calculating logarithms, with historical notices relating to the contributions of
Oughtred and others to mathematical notation. The Quarterly journal of pure
and applied mathematics, 46:125–197, 1915.
[39] James Whitbread Lee Glaisher. On early tables of logarithms and the early
history of logarithms. The Quarterly journal of pure and applied mathematics,
48:151–192, 1920.
[40] Herman Heine Goldstine. A history of numerical analysis from the 16th through
the 19th century. New York: Springer, 1977.
28
[41] Edmund Gunter. Canon triangulorum, sive tabulæ sinuum et tangentium
artificialium ad radium 10000,0000.& ad scrupula prima quadrantis. London:
William Jones, 1620. [The tables were reconstructed by D. Roegel in 2010. [84]]
[42] Jean-Pierre Hairault. Calcul des logarithmes décimaux par Henry Briggs. In
Barbin et al. [5], pages 113–129.
[43] Anders Hald. A history of probability and statistics and their applications before
1750. New York: John Wiley & Sons, 2003.
[44] James Orchard Halliwell, editor. Rara mathematica; or, a collection of treatises
on the mathematics and subjects connected with them, from ancient inedited
manuscripts. London: John William Parker, 1839.
[45] D. M. Hallowes. Henry Briggs, mathematician. Transactions of the Halifax
Antiquarian Society, pages 79–92, 1962.
[46] James Henderson. Bibliotheca tabularum mathematicarum, being a descriptive
catalogue of mathematical tables. Part I: Logarithmic tables (A. Logarithms of
numbers), volume XIII of Tracts for computers. London: Cambridge University
Press, 1926.
[47] Christopher Hill. Intellectual origins of the English Revolution revisited. Oxford:
Clarendon press, 1997.
[48] Charles Hutton. Mathematical tables: containing common, hyperbolic, and logistic
logarithms, also sines, tangents, secants, and versed-sines, etc. London: G. G. J.,
J. Robinson, and R. Baldwin, 1785.
[49] G. Huxley. Briggs, Henry. In Charles Coulston Gillispie, editor, Dictionary of
Scientific Biography, volume 2, pages 461–463. New York: Charles Scribner’s Sons.
[50] Graham Jagger. The making of logarithm tables. In Martin Campbell-Kelly,
Mary Croarken, Raymond Flood, and Eleanor Robson, editors, The history of
mathematical tables: from Sumer to spreadsheets, pages 48–77. Oxford: Oxford
University Press, 2003.
[51] Graham Jagger. The will of Henry Briggs. BSHM Bulletin: Journal of the British
Society for the History of Mathematics, 21(2):127–131, July 2006.
[52] Wolfgang Kaunzner. Über Henry Briggs, den Schöpfer der Zehnerlogarithmen. In
Rainer Gebhardt, editor, Visier- und Rechenbücher der frühen Neuzeit, volume 19
of Schriften des Adam-Ries-Bundes e.V. Annaberg-Buchholz, pages 179–214.
Annaberg-Buchholz: Adam-Ries-Bund, 2008.
[53] Johannes Kepler, John Napier, and Henry Briggs. Les milles logarithmes ; etc.
Bordeaux: Jean Peyroux, 1993. [French translation of Kepler’s tables and Neper’s
descriptio by Jean Peyroux.]
[54] Cargill Gilston Knott, editor. Napier Tercentenary Memorial Volume. London:
Longmans, Green and company, 1915.
29
[55] Pierre Alexandre Francisque Lefort. Description des grandes tables logarithmiques
et trigonométriques, calculées au bureau du cadastre, sous la direction de Prony,
et exposition des méthodes et procédés mis en usage pour leur construction.
Annales de l’Observatoire impérial de Paris, 4 (supplément):123–150, 1858.
[56] Pierre Alexandre Francisque Lefort. Note sur les deux exemplaires manuscrits des
grandes tables logarithmiques et trigonométriques, calculées au bureau du
cadastre, sous la direction de Prony. Comptes rendus hebdomadaires des séances
de l’Académie des sciences, 46:994–999, janvier-juin 1858.
[57] Adrien Marie Legendre. Sur une méthode d’interpolation employée par Briggs,
dans la construction de ses grandes tables trigonométriques. In Additions à la
Connaissance des tems, ou des mouvemens célestes, à l’usage des astronomes et
des navigateurs, pour l’an 1817, pages 219–222. Paris: Veuve Courcier, 1815.
[58] Martha List and Volker Bialas. Die Coss von Jost Bürgi in der Redaktion von
Johannes Kepler. Ein Beitrag zur frühen Algebra, volume 5 (Neue Folge) of Nova
Kepleriana. München: Bayerische Akademie der Wissenschaften, 1973.
[59] Sydney Lupton. Notes on the radix method of calculating logarithms. The
Mathematical Gazette, 7(106):147–150, July 1913.
[60] Sydney Lupton. Notes on the radix method of calculating logarithms (continued).
The Mathematical Gazette, 7(107):170–173, October 1913.
[61] Noel Malcolm and Jacqueline Stedall, editors. John Pell (1611–1685) and his
correspondence with Sir Charles Cavendish: the mental world of an early modern
mathematician. Oxford: Oxford university press, 2005.
[62] Thomas Manning. New method of computing logarithms. Philosophical
Transactions of the Royal Society of London, 96:327–341, 1806. [description of a
variant of the radix method]
[63] Andrei Andreivich Markov. Differenzenrechnung. Leipzig: B. G. Teubner, 1896.
[Translated from the Russian.]
[64] Francis Maseres. Scriptores logarithmici, volume 2. London: J. Davis, 1791.
[65] Frédéric Maurice. Mémoire sur les interpolations, contenant surtout, avec une
exposition fort simple de leur théorie, dans ce qu’elle a de plus utile pour les
applications, la démonstration générale et complète de la méthode de
quinti-section de Briggs et de celle de Mouton, quand les indices sont
équidifférents, et du procédé exposé par Newton, dans ses Principes, quand les
indices sont quelconques. In Additions à la Connaissance des temps ou des
mouvements célestes, à l’usage des astronomes et des navigateurs, pour l’an 1847,
pages 181–222. Paris: Bachelier, 1844. [A summary is given in the Comptes rendus
hebdomadaires des séances de l’Académie des sciences, 19(2), 8 July 1844, pp. 81–85, and the
entire article is translated in the Journal of the Institute of Actuaries and Assurance Magazine,
volume 14, 1869, pp. 1–36.]
30
[66] Erik Meijering. A chronology of interpolation: from ancient astronomy to modern
signal and image processing. Proceedings of the IEEE, 90(3):319–342, March 2002.
[67] Leo Miller. Milton and Vlacq. Papers of the Bibliographical Society of America,
73:145–208, 1979.
[68] John Napier. Mirifici logarithmorum canonis descriptio. Edinburgh: Andrew
Hart, 1614.
[69] John Napier. A description of the admirable table of logarithmes. London, 1616.
[English translation of [68] by Edward Wright, reprinted in 1969 by Da Capo Press, New York.
A second edition appeared in 1618.]
[70] John Napier. Mirifici logarithmorum canonis constructio. Edinburgh: Andrew
Hart, 1619. [Reprinted in [71] and translated in [72]. A modern English translation by Ian
Bruce is available on the web.]
[71] John Napier. “Logarithmorum canonis descriptio” and “Mirifici logarithmorum
canonis constructio”. Lyon: Barthélemi Vincent, 1620. [Reprint of Napier’s descriptio
and constructio. At least the constructio was reprinted by A. Hermann in 1895.]
[72] John Napier. The construction of the wonderful canon of logarithms. Edinburgh:
William Blackwood and sons, 1889. [Translation of [70] by William Rae Macdonald.]
[73] Katherine Neal. Mathematics and empire, navigation and exploration: Henry
Briggs and the northwest passage voyages of 1631. Isis, 93(3):435–453, 2002.
[74] Richard Norwood. Trigonometrie. Or, the doctrine of triangles. London: William
Jones, 1631. [Reprinted in 1971 by Theatrum Orbis Terratum (Amsterdam). Not seen.]
[75] Ludwig Oechslin. Jost Bürgi. Luzern: Verlag Ineichen, 2000.
[76] Robert Keith Otnes. How Briggs computed logarithms. Journal of the Oughtred
Society, 4(2):26–27, 1995. [not seen]
[77] Penny cyclopædia. Briggs (Henry). In The Penny cyclopædia of the society for
the diffusion of useful knowledge, volume V, pages 422–423. London: Charles
Knight and Co., 1836.
[78] Alfred Israel Pringsheim, Georg Faber, and Jules Molk. Analyse algébrique. In
Encyclopédie des sciences mathématiques pures et appliquées, tome II, volume 2,
fascicule 1, pages 1–93. Paris: Gauthier-Villars, 1911. [See p. 54 for remarks on Briggs.]
[79] Jean-Charles Rodolphe Radau. Études sur les formules d’interpolation. Bulletin
Astronomique, Série I, 8:273–294, 1891.
[80] Stephen Jordan Rigaud, editor. Correspondence of scientific men of the
seventeenth century, including letters of Barrow, Flamsteed, Wallis, and Newton,
printed from the originals in the collection of the right honourable the Earl of
Macclesfield. Oxford: university press, 1841. [2 volumes]
31
[81] Denis Roegel. A reconstruction of Adriaan Vlacq’s tables in the Trigonometria
artificialis (1633). Technical report, LORIA, Nancy, 2010. [This is a recalculation of
the tables of [106].]
[82] Denis Roegel. A reconstruction of Briggs’s Logarithmorum chilias prima (1617).
Technical report, LORIA, Nancy, 2010. [This is a recalculation of the tables of [9].]
[83] Denis Roegel. A reconstruction of De Decker-Vlacq’s tables in the Arithmetica
logarithmica (1628). Technical report, LORIA, Nancy, 2010. [This is a recalculation
of the tables of [105].]
[84] Denis Roegel. A reconstruction of Gunter’s Canon triangulorum (1620).
Technical report, LORIA, Nancy, 2010. [This is a recalculation of the tables of [41].]
[85] Denis Roegel. A reconstruction of the tables of Briggs and Gellibrand’s
Trigonometria Britannica (1633). Technical report, LORIA, Nancy, 2010. [This is
a recalculation of the tables of [11].]
[86] Denis Roegel. A reconstruction of the tables of Thompson’s Logarithmetica
Britannica (1952). Technical report, LORIA, Nancy, 2010. [This is a unpublished
reconstruction of the tables in [101], not available for copyright reasons.]
[87] Denis Roegel. Briggs’ ideal canon of logarithms. Technical report, LORIA, Nancy,
2010. [This is a recalculation of the tables of [10], including the gap left empty by Briggs.]
[88] Denis Roegel. Bürgi’s Progress Tabulen (1620): logarithmic tables without
logarithms. Technical report, LORIA, Nancy, 2010.
[89] Denis Roegel. Napier’s ideal construction of the logarithms. Technical report,
LORIA, Nancy, 2010.
[90] Denis Roegel. The great logarithmic and trigonometric tables of the French
Cadastre: a preliminary investigation. Technical report, LORIA, Nancy, 2010.
[91] Edward Sang. On last-place errors in Vlacq. Nature, 42(1094):593, 1890.
[92] Demetrius Seliwanoff. Lehrbuch der Differenzenrechnung. Leipzig: B. G. Teubner,
1904.
[93] John William Shirley. Thomas Harriot, a biography. Oxford: Oxford university
press, 1983. [not seen]
[94] Thomas Smith. Vitæ quorundam eruditissimorum et illustrium virorum. London:
David Mortier, 1707. [Contains a 16-pages separately paginated biography of Briggs
“Commentariolus de vita et studiis clarissimi & doctissimi viri, D. Henrici Briggii, olim
geometriæ in academia Oxoniensi professoris saviliani,” of which a translation is given
pp. lxvii–lxxvii of volume 1 of [101].]
[95] Thomas Sonar. The grave of Henry Briggs. The Mathematical Intelligencer,
22(3):58–59, September 2000.
32
[96] Thomas Sonar. Der fromme Tafelmacher : Die frühen Arbeiten des Henry Briggs.
Berlin: Logos Verlag, 2002.
[97] Thomas Sonar. Die Berechnung der Logarithmentafeln durch Napier und Briggs,
2004.
[98] Euclid Speidell. Logarithmotechnia, or, the making of numbers called logarithms
to twenty five places from a geometrical figure. London: Henry Clark, 1688.
[reproduced by Maseres [64]]
[99] Dirk Jan Struik. Vlacq, Adriaan. In Charles Coulston Gillispie, editor, Dictionary
of Scientific Biography, volume 14, pages 51–52. New York: Charles Scribner’s
Sons.
[100] Alexander John Thompson. Henry Briggs and his work on logarithms. The
American Mathematical Monthly, 32(3):129–131, March 1925.
[101] Alexander John Thompson. Logarithmetica Britannica, being a standard table of
logarithms to twenty decimal places of the numbers 10,000 to 100,000. Cambridge:
University press, 1952. [2 volumes, unpublished reconstruction by D. Roegel in 2010 [86].]
[102] Herbert Westren Turnbull. James Gregory: a study in the early history of
interpolation. Proceedings of the Edinburgh Mathematical Society (Series 2),
3(3):151–172, 1933.
[103] Otto E. van Poelje. Adriaen Vlacq and Ezechiel de Decker: Dutch contributors to
the early tables of Briggsian logarithms. Journal of the Oughtred Society,
14(1):30–40, 2005.
[104] Erik Vestergaard. Henry Briggs’ differensmetode. Normat — Nordisk Matematisk
Tidsskrift, 45(2):49–61, 1997.
[105] Adriaan Vlacq. Arithmetica logarithmica. Gouda: Pieter Rammazeyn, 1628. [The
introduction was reprinted in 1976 by Olms and the tables were reconstructed by D. Roegel in
2010. [83]]
[106] Adriaan Vlacq. Trigonometria artificialis. Gouda: Pieter Rammazeyn, 1633. [The
tables were reconstructed by D. Roegel in 2010. [81]]
[107] John Ward. The lives of the professors of Gresham College. London: John Moore,
1740. [pp. 120–129 on Briggs. This part was reprinted in The Monthly Magazine, vol. 28,
no. 190, 1st October 1809, pp. 275–281.]
[108] John Wells. Sciographia, or the art of shadovves... All performed, by the doctrine
of triangles... and by helpe of... logarithmes. London: T. Harper, 1635. [not seen]
[109] Derek Thomas Whiteside. Henry Briggs: The binomial theorem anticipated. The
Mathematical Gazette, 45(351):9–12, February 1961.
[110] Derek Thomas Whiteside. Newton’s discovery of the general binomial theorem.
The Mathematical Gazette, 45(353):175–180, October 1961.
33
[111] Derek Thomas Whiteside. Patterns of mathematical thought in the later
seventeenth century. Archive for History of Exact Sciences, 1:179–388, 1961.
[112] Derek Thomas Whiteside, editor. The Mathematical Papers of Isaac Newton:
Volume I, 1664–1666. Cambridge: Cambridge University Press, 1967.
[113] Derek Thomas Whiteside, editor. The Mathematical Papers of Isaac Newton:
Volume III, 1670–1673. Cambridge: Cambridge University Press, 1969.
[114] Derek Thomas Whiteside, editor. The Mathematical Papers of Isaac Newton:
Volume IV, 1674–1684. Cambridge: Cambridge University Press, 1971.
[115] Derek Thomas Whiteside, editor. The Mathematical Papers of Isaac Newton:
Volume VII, 1691–1695. Cambridge: Cambridge University Press, 1976.
[116] Thomas Whittaker. Henry Briggs. In Dictionary of National Biography, volume 2,
pages 1234–1235. London: Smith, Elder, & Co., 1908. [volume 6 (1886), pp. 326–327,
in the first edition]
[117] James K. Whittemore. The calculation of logarithms. The Annals of
Mathematics, Second Series 9(1):1–28, October 1907. [This article describes Weddle’s
method, which is a variant of the radix method.]
[118] J. Hill Williams. Briggs’s method of interpolation; being a translation of the 13th
chapter and part of the 12th of the preface to the “Arithmetica Logarithmica”.
Journal of the Institute of Actuaries and Assurance Magazine, 14:73–88, 1869.
[119] Robin Wilson. The oldest mathematical chair in Britain. EMS Newsletter,
64:26–29, June 2007.
[120] Edward Wright. Certaine errors in nauigation, detected and corrected. London:
Felix Kingston, 1610. [contains several tables computed by Briggs]
34
Briggs’ 1624 table of logarithms (reconstruction, D. Roegel, 2010)
Chilias prima.
Num.
absolu.

Logarithmi.
,,,
Num.
absolu.

,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,
,,
,,,

,,,

,,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,,
,,,

,,


,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,


,,
,,
,,
,,,
,,,
,,
,,

,,,

,,
,,,

,,
,,

,,,
,,
,,
,,,

,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,
,,,
,,,

,,


,,
,,
,,
,,,
,,,
,,
,,


,,
,,
,,,
,,,

,,

,,,
,,
,,


,,
,,
,,,
,,
,,
,,

,,,

,,

,,
,,
,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
Logarithmi.
,,
,,
,,

,,,

,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
,,
,,,
,,,
Num.
absolu.

,,
,,

Logarithmi.
,,

,,,
,,

35
Briggs’ 1624 table of logarithms (reconstruction, D. Roegel, 2010)
Chilias prima.
Num.
absolu.

Logarithmi.
,,,
Num.
absolu.

,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,
,,
,,,

,,,

,,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,,
,,,

,,


,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,


,,
,,
,,
,,,
,,,
,,
,,

,,,

,,
,,,

,,
,,

,,,
,,
,,
,,,

,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,
,,,
,,,

,,


,,
,,
,,
,,,
,,,
,,
,,


,,
,,
,,,
,,,

,,

,,,
,,
,,


,,
,,
,,,
,,
,,
,,

,,,

,,

,,
,,
,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
Logarithmi.
,,
,,
,,

,,,

,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
,,
,,,
,,,
Num.
absolu.

,,
,,

Logarithmi.
,,

,,,
,,

36
Briggs’ 1624 table of logarithms (reconstruction, D. Roegel, 2010)
Chilias prima.
Num.
absolu.

Logarithmi.
,,,
Num.
absolu.

,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,
,,
,,,

,,,

,,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,,
,,,

,,


,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,


,,
,,
,,
,,,
,,,
,,
,,

,,,

,,
,,,

,,
,,

,,,
,,
,,
,,,

,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,
,,,
,,,

,,


,,
,,
,,
,,,
,,,
,,
,,


,,
,,
,,,
,,,

,,

,,,
,,
,,


,,
,,
,,,
,,
,,
,,

,,,

,,

,,
,,
,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
Logarithmi.
,,
,,
,,

,,,

,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
,,
,,,
,,,
Num.
absolu.

,,
,,

Logarithmi.
,,

,,,
,,

37
Briggs’ 1624 table of logarithms (reconstruction, D. Roegel, 2010)
Chilias prima.
Num.
absolu.

Logarithmi.
,,,
Num.
absolu.

,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,
,,
,,,

,,,

,,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,,
,,,

,,


,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,


,,
,,
,,
,,,
,,,
,,
,,

,,,

,,
,,,

,,
,,

,,,
,,
,,
,,,

,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,
,,,
,,,

,,


,,
,,
,,
,,,
,,,
,,
,,


,,
,,
,,,
,,,

,,

,,,
,,
,,


,,
,,
,,,
,,
,,
,,

,,,

,,

,,
,,
,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
Logarithmi.
,,
,,
,,

,,,

,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
,,
,,,
,,,
Num.
absolu.

,,
,,

Logarithmi.
,,

,,,
,,

38
Briggs’ 1624 table of logarithms (reconstruction, D. Roegel, 2010)
Chilias prima.
Num.
absolu.

Logarithmi.
,,,
Num.
absolu.

,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,
,,
,,,

,,,

,,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,,
,,,

,,


,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,


,,
,,
,,
,,,
,,,
,,
,,

,,,

,,
,,,

,,
,,

,,,
,,
,,
,,,

,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,
,,,
,,,

,,


,,
,,
,,
,,,
,,,
,,
,,


,,
,,
,,,
,,,

,,

,,,
,,
,,


,,
,,
,,,
,,
,,
,,

,,,

,,

,,
,,
,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
Logarithmi.
,,
,,
,,

,,,

,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
,,
,,,
,,,
Num.
absolu.

,,
,,

Logarithmi.
,,

,,,
,,

39
Briggs’ 1624 table of logarithms (reconstruction, D. Roegel, 2010)
Chilias prima.
Num.
absolu.

Logarithmi.
,,,
Num.
absolu.

,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,
,,
,,,

,,,

,,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,,
,,,

,,


,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,


,,
,,
,,
,,,
,,,
,,
,,

,,,

,,
,,,

,,
,,

,,,
,,
,,
,,,

,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,
,,,
,,,

,,


,,
,,
,,
,,,
,,,
,,
,,


,,
,,
,,,
,,,

,,

,,,
,,
,,


,,
,,
,,,
,,
,,
,,

,,,

,,

,,
,,
,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
Logarithmi.
,,
,,
,,

,,,

,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
,,
,,,
,,,
Num.
absolu.

,,
,,

Logarithmi.
,,

,,,
,,

40
Briggs’ 1624 table of logarithms (reconstruction, D. Roegel, 2010)
Chilias prima.
Num.
absolu.

Logarithmi.
,,,
Num.
absolu.

,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,
,,
,,,

,,,

,,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,,
,,,

,,


,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,


,,
,,
,,
,,,
,,,
,,
,,

,,,

,,
,,,

,,
,,

,,,
,,
,,
,,,

,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,
,,,
,,,

,,


,,
,,
,,
,,,
,,,
,,
,,


,,
,,
,,,
,,,

,,

,,,
,,
,,


,,
,,
,,,
,,
,,
,,

,,,

,,

,,
,,
,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
Logarithmi.
,,
,,
,,

,,,

,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
,,
,,,
,,,
Num.
absolu.

,,
,,

Logarithmi.
,,

,,,
,,

41
Briggs’ 1624 table of logarithms (reconstruction, D. Roegel, 2010)
Chilias prima.
Num.
absolu.

Logarithmi.
,,,
Num.
absolu.

,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,
,,
,,,

,,,

,,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,,
,,,

,,


,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,


,,
,,
,,
,,,
,,,
,,
,,

,,,

,,
,,,

,,
,,

,,,
,,
,,
,,,

,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,
,,,
,,,

,,


,,
,,
,,
,,,
,,,
,,
,,


,,
,,
,,,
,,,

,,

,,,
,,
,,


,,
,,
,,,
,,
,,
,,

,,,

,,

,,
,,
,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
Logarithmi.
,,
,,
,,

,,,

,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
,,
,,,
,,,
Num.
absolu.

,,
,,

Logarithmi.
,,

,,,
,,

42
Briggs’ 1624 table of logarithms (reconstruction, D. Roegel, 2010)
Chilias prima.
Num.
absolu.

Logarithmi.
,,,
Num.
absolu.

,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,
,,
,,,

,,,

,,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,,
,,,

,,


,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,


,,
,,
,,
,,,
,,,
,,
,,

,,,

,,
,,,

,,
,,

,,,
,,
,,
,,,

,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,
,,,
,,,

,,


,,
,,
,,
,,,
,,,
,,
,,


,,
,,
,,,
,,,

,,

,,,
,,
,,


,,
,,
,,,
,,
,,
,,

,,,

,,

,,
,,
,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
Logarithmi.
,,
,,
,,

,,,

,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
,,
,,,
,,,
Num.
absolu.

,,
,,

Logarithmi.
,,

,,,
,,

43
Briggs’ 1624 table of logarithms (reconstruction, D. Roegel, 2010)
Chilias prima.
Num.
absolu.

Logarithmi.
,,,
Num.
absolu.

,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,
,,
,,,

,,,

,,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,,
,,,

,,


,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,


,,
,,
,,
,,,
,,,
,,
,,

,,,

,,
,,,

,,
,,

,,,
,,
,,
,,,

,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,
,,,
,,,

,,


,,
,,
,,
,,,
,,,
,,
,,


,,
,,
,,,
,,,

,,

,,,
,,
,,


,,
,,
,,,
,,
,,
,,

,,,

,,

,,
,,
,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
Logarithmi.
,,
,,
,,

,,,

,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
,,
,,,
,,,
Num.
absolu.

,,
,,

Logarithmi.
,,

,,,
,,

44
Briggs’ 1624 table of logarithms (reconstruction, D. Roegel, 2010)
Chilias secunda.
Num.
absolu.

Logarithmi.
,,,
Num.
absolu.

,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,
,,
,,,

,,,

,,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,,
,,,

,,


,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,


,,
,,
,,
,,,
,,,
,,
,,

,,,

,,
,,,

,,
,,

,,,
,,
,,
,,,

,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,
,,,
,,,

,,


,,
,,
,,
,,,
,,,
,,
,,


,,
,,
,,,
,,,

,,

,,,
,,
,,


,,
,,
,,,
,,
,,
,,

,,,

,,

,,
,,
,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
Logarithmi.
,,
,,
,,

,,,

,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
,,
,,,
,,,
Num.
absolu.

,,
,,

Logarithmi.
,,

,,,
,,

45
Briggs’ 1624 table of logarithms (reconstruction, D. Roegel, 2010)
Chilias secunda.
Num.
absolu.

Logarithmi.
,,,
Num.
absolu.

,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,
,,
,,,

,,,

,,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,,
,,,

,,


,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,


,,
,,
,,
,,,
,,,
,,
,,

,,,

,,
,,,

,,
,,

,,,
,,
,,
,,,

,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,
,,,
,,,

,,


,,
,,
,,
,,,
,,,
,,
,,


,,
,,
,,,
,,,

,,

,,,
,,
,,


,,
,,
,,,
,,
,,
,,

,,,

,,

,,
,,
,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
Logarithmi.
,,
,,
,,

,,,

,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
,,
,,,
,,,
Num.
absolu.

,,
,,

Logarithmi.
,,

,,,
,,

46
Briggs’ 1624 table of logarithms (reconstruction, D. Roegel, 2010)
Chilias secunda.
Num.
absolu.

Logarithmi.
,,,
Num.
absolu.

,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,
,,
,,,

,,,

,,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,,
,,,

,,


,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,


,,
,,
,,
,,,
,,,
,,
,,

,,,

,,
,,,

,,
,,

,,,
,,
,,
,,,

,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,
,,,
,,,

,,


,,
,,
,,
,,,
,,,
,,
,,


,,
,,
,,,
,,,

,,

,,,
,,
,,


,,
,,
,,,
,,
,,
,,

,,,

,,

,,
,,
,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
Logarithmi.
,,
,,
,,

,,,

,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
,,
,,,
,,,
Num.
absolu.

,,
,,

Logarithmi.
,,

,,,
,,

47
Briggs’ 1624 table of logarithms (reconstruction, D. Roegel, 2010)
Chilias secunda.
Num.
absolu.

Logarithmi.
,,,
Num.
absolu.

,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,
,,
,,,

,,,

,,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,,
,,,

,,


,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,


,,
,,
,,
,,,
,,,
,,
,,

,,,

,,
,,,

,,
,,

,,,
,,
,,
,,,

,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,
,,,
,,,

,,


,,
,,
,,
,,,
,,,
,,
,,


,,
,,
,,,
,,,

,,

,,,
,,
,,


,,
,,
,,,
,,
,,
,,

,,,

,,

,,
,,
,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
Logarithmi.
,,
,,
,,

,,,

,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
,,
,,,
,,,
Num.
absolu.

,,
,,

Logarithmi.
,,

,,,
,,

48
Briggs’ 1624 table of logarithms (reconstruction, D. Roegel, 2010)
Chilias secunda.
Num.
absolu.

Logarithmi.
,,,
Num.
absolu.

,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,
,,
,,,

,,,

,,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,,
,,,

,,


,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,


,,
,,
,,
,,,
,,,
,,
,,

,,,

,,
,,,

,,
,,

,,,
,,
,,
,,,

,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,
,,,
,,,

,,


,,
,,
,,
,,,
,,,
,,
,,


,,
,,
,,,
,,,

,,

,,,
,,
,,


,,
,,
,,,
,,
,,
,,

,,,

,,

,,
,,
,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
Logarithmi.
,,
,,
,,

,,,

,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
,,
,,,
,,,
Num.
absolu.

,,
,,

Logarithmi.
,,

,,,
,,

49
Briggs’ 1624 table of logarithms (reconstruction, D. Roegel, 2010)
Chilias secunda.
Num.
absolu.

Logarithmi.
,,,
Num.
absolu.

,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,
,,
,,,

,,,

,,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,,
,,,

,,


,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,


,,
,,
,,
,,,
,,,
,,
,,

,,,

,,
,,,

,,
,,

,,,
,,
,,
,,,

,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,
,,,
,,,

,,


,,
,,
,,
,,,
,,,
,,
,,


,,
,,
,,,
,,,

,,

,,,
,,
,,


,,
,,
,,,
,,
,,
,,

,,,

,,

,,
,,
,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
Logarithmi.
,,
,,
,,

,,,

,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
,,
,,,
,,,
Num.
absolu.

,,
,,

Logarithmi.
,,

,,,
,,

50
Briggs’ 1624 table of logarithms (reconstruction, D. Roegel, 2010)
Chilias secunda.
Num.
absolu.

Logarithmi.
,,,
Num.
absolu.

,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,
,,
,,,

,,,

,,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,,
,,,

,,


,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,


,,
,,
,,
,,,
,,,
,,
,,

,,,

,,
,,,

,,
,,

,,,
,,
,,
,,,

,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,
,,,
,,,

,,


,,
,,
,,
,,,
,,,
,,
,,


,,
,,
,,,
,,,

,,

,,,
,,
,,


,,
,,
,,,
,,
,,
,,

,,,

,,

,,
,,
,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
Logarithmi.
,,
,,
,,

,,,

,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
,,
,,,
,,,
Num.
absolu.

,,
,,

Logarithmi.
,,

,,,
,,

51
Briggs’ 1624 table of logarithms (reconstruction, D. Roegel, 2010)
Chilias secunda.
Num.
absolu.

Logarithmi.
,,,
Num.
absolu.

,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,
,,
,,,

,,,

,,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,,
,,,

,,


,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,


,,
,,
,,
,,,
,,,
,,
,,

,,,

,,
,,,

,,
,,

,,,
,,
,,
,,,

,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,
,,,
,,,

,,


,,
,,
,,
,,,
,,,
,,
,,


,,
,,
,,,
,,,

,,

,,,
,,
,,


,,
,,
,,,
,,
,,
,,

,,,

,,

,,
,,
,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
Logarithmi.
,,
,,
,,

,,,

,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
,,
,,,
,,,
Num.
absolu.

,,
,,

Logarithmi.
,,

,,,
,,

52
Briggs’ 1624 table of logarithms (reconstruction, D. Roegel, 2010)
Chilias secunda.
Num.
absolu.

Logarithmi.
,,,
Num.
absolu.

,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,
,,
,,,

,,,

,,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,,
,,,

,,


,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,


,,
,,
,,
,,,
,,,
,,
,,

,,,

,,
,,,

,,
,,

,,,
,,
,,
,,,

,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,
,,,
,,,

,,


,,
,,
,,
,,,
,,,
,,
,,


,,
,,
,,,
,,,

,,

,,,
,,
,,


,,
,,
,,,
,,
,,
,,

,,,

,,

,,
,,
,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
Logarithmi.
,,
,,
,,

,,,

,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
,,
,,,
,,,
Num.
absolu.

,,
,,

Logarithmi.
,,

,,,
,,

53
Briggs’ 1624 table of logarithms (reconstruction, D. Roegel, 2010)
Chilias secunda.
Num.
absolu.

Logarithmi.
,,,
Num.
absolu.

,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,
,,
,,,

,,,

,,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,,
,,,

,,


,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,


,,
,,
,,
,,,
,,,
,,
,,

,,,

,,
,,,

,,
,,

,,,
,,
,,
,,,

,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,
,,,
,,,

,,


,,
,,
,,
,,,
,,,
,,
,,


,,
,,
,,,
,,,

,,

,,,
,,
,,


,,
,,
,,,
,,
,,
,,

,,,

,,

,,
,,
,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
Logarithmi.
,,
,,
,,

,,,

,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
,,
,,,
,,,
Num.
absolu.

,,
,,

Logarithmi.
,,

,,,
,,

54
Briggs’ 1624 table of logarithms (reconstruction, D. Roegel, 2010)
Chilias tertia.
Num.
absolu.

Logarithmi.
,,,
Num.
absolu.

,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,
,,
,,,

,,,

,,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,,
,,,

,,


,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,


,,
,,
,,
,,,
,,,
,,
,,

,,,

,,
,,,

,,
,,

,,,
,,
,,
,,,

,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,
,,,
,,,

,,


,,
,,
,,
,,,
,,,
,,
,,


,,
,,
,,,
,,,

,,

,,,
,,
,,


,,
,,
,,,
,,
,,
,,

,,,

,,

,,
,,
,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
Logarithmi.
,,
,,
,,

,,,

,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
,,
,,,
,,,
Num.
absolu.

,,
,,

Logarithmi.
,,

,,,
,,

55
Briggs’ 1624 table of logarithms (reconstruction, D. Roegel, 2010)
Chilias tertia.
Num.
absolu.

Logarithmi.
,,,
Num.
absolu.

,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,
,,
,,,

,,,

,,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,,
,,,

,,


,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,


,,
,,
,,
,,,
,,,
,,
,,

,,,

,,
,,,

,,
,,

,,,
,,
,,
,,,

,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,
,,,
,,,

,,


,,
,,
,,
,,,
,,,
,,
,,


,,
,,
,,,
,,,

,,

,,,
,,
,,


,,
,,
,,,
,,
,,
,,

,,,

,,

,,
,,
,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
Logarithmi.
,,
,,
,,

,,,

,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
,,
,,,
,,,
Num.
absolu.

,,
,,

Logarithmi.
,,

,,,
,,

56
Briggs’ 1624 table of logarithms (reconstruction, D. Roegel, 2010)
Chilias tertia.
Num.
absolu.

Logarithmi.
,,,
Num.
absolu.

,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,
,,
,,,

,,,

,,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,,
,,,

,,


,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,


,,
,,
,,
,,,
,,,
,,
,,

,,,

,,
,,,

,,
,,

,,,
,,
,,
,,,

,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,
,,,
,,,

,,


,,
,,
,,
,,,
,,,
,,
,,


,,
,,
,,,
,,,

,,

,,,
,,
,,


,,
,,
,,,
,,
,,
,,

,,,

,,

,,
,,
,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
Logarithmi.
,,
,,
,,

,,,

,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
,,
,,,
,,,
Num.
absolu.

,,
,,

Logarithmi.
,,

,,,
,,

57
Briggs’ 1624 table of logarithms (reconstruction, D. Roegel, 2010)
Chilias tertia.
Num.
absolu.

Logarithmi.
,,,
Num.
absolu.

,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,
,,
,,,

,,,

,,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,,
,,,

,,


,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,


,,
,,
,,
,,,
,,,
,,
,,

,,,

,,
,,,

,,
,,

,,,
,,
,,
,,,

,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,
,,,
,,,

,,


,,
,,
,,
,,,
,,,
,,
,,


,,
,,
,,,
,,,

,,

,,,
,,
,,


,,
,,
,,,
,,
,,
,,

,,,

,,

,,
,,
,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
Logarithmi.
,,
,,
,,

,,,

,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
,,
,,,
,,,
Num.
absolu.

,,
,,

Logarithmi.
,,

,,,
,,

58
Briggs’ 1624 table of logarithms (reconstruction, D. Roegel, 2010)
Chilias tertia.
Num.
absolu.

Logarithmi.
,,,
Num.
absolu.

,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,
,,
,,,

,,,

,,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,,
,,,

,,


,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,


,,
,,
,,
,,,
,,,
,,
,,

,,,

,,
,,,

,,
,,

,,,
,,
,,
,,,

,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,
,,,
,,,

,,


,,
,,
,,
,,,
,,,
,,
,,


,,
,,
,,,
,,,

,,

,,,
,,
,,


,,
,,
,,,
,,
,,
,,

,,,

,,

,,
,,
,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
Logarithmi.
,,
,,
,,

,,,

,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
,,
,,,
,,,
Num.
absolu.

,,
,,

Logarithmi.
,,

,,,
,,

59
Briggs’ 1624 table of logarithms (reconstruction, D. Roegel, 2010)
Chilias tertia.
Num.
absolu.

Logarithmi.
,,,
Num.
absolu.

,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,
,,
,,,

,,,

,,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,,
,,,

,,


,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,


,,
,,
,,
,,,
,,,
,,
,,

,,,

,,
,,,

,,
,,

,,,
,,
,,
,,,

,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,
,,,
,,,

,,


,,
,,
,,
,,,
,,,
,,
,,


,,
,,
,,,
,,,

,,

,,,
,,
,,


,,
,,
,,,
,,
,,
,,

,,,

,,

,,
,,
,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
Logarithmi.
,,
,,
,,

,,,

,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
,,
,,,
,,,
Num.
absolu.

,,
,,

Logarithmi.
,,

,,,
,,

60
Briggs’ 1624 table of logarithms (reconstruction, D. Roegel, 2010)
Chilias tertia.
Num.
absolu.

Logarithmi.
,,,
Num.
absolu.

,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,
,,
,,,

,,,

,,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,,
,,,

,,


,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,


,,
,,
,,
,,,
,,,
,,
,,

,,,

,,
,,,

,,
,,

,,,
,,
,,
,,,

,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,
,,,
,,,

,,


,,
,,
,,
,,,
,,,
,,
,,


,,
,,
,,,
,,,

,,

,,,
,,
,,


,,
,,
,,,
,,
,,
,,

,,,

,,

,,
,,
,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
Logarithmi.
,,
,,
,,

,,,

,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
,,
,,,
,,,
Num.
absolu.

,,
,,

Logarithmi.
,,

,,,
,,

61
Briggs’ 1624 table of logarithms (reconstruction, D. Roegel, 2010)
Chilias tertia.
Num.
absolu.

Logarithmi.
,,,
Num.
absolu.

,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,
,,
,,,

,,,

,,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,,
,,,

,,


,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,


,,
,,
,,
,,,
,,,
,,
,,

,,,

,,
,,,

,,
,,

,,,
,,
,,
,,,

,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,
,,,
,,,

,,


,,
,,
,,
,,,
,,,
,,
,,


,,
,,
,,,
,,,

,,

,,,
,,
,,


,,
,,
,,,
,,
,,
,,

,,,

,,

,,
,,
,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
Logarithmi.
,,
,,
,,

,,,

,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
,,
,,,
,,,
Num.
absolu.

,,
,,

Logarithmi.
,,

,,,
,,

62
Briggs’ 1624 table of logarithms (reconstruction, D. Roegel, 2010)
Chilias tertia.
Num.
absolu.

Logarithmi.
,,,
Num.
absolu.

,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,
,,
,,,

,,,

,,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,,
,,,

,,


,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,


,,
,,
,,
,,,
,,,
,,
,,

,,,

,,
,,,

,,
,,

,,,
,,
,,
,,,

,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,
,,,
,,,

,,


,,
,,
,,
,,,
,,,
,,
,,


,,
,,
,,,
,,,

,,

,,,
,,
,,


,,
,,
,,,
,,
,,
,,

,,,

,,

,,
,,
,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
Logarithmi.
,,
,,
,,

,,,

,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
,,
,,,
,,,
Num.
absolu.

,,
,,

Logarithmi.
,,

,,,
,,

63
Briggs’ 1624 table of logarithms (reconstruction, D. Roegel, 2010)
Chilias tertia.
Num.
absolu.

Logarithmi.
,,,
Num.
absolu.

,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,
,,
,,,

,,,

,,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,,
,,,

,,


,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,


,,
,,
,,
,,,
,,,
,,
,,

,,,

,,
,,,

,,
,,

,,,
,,
,,
,,,

,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,
,,,
,,,

,,


,,
,,
,,
,,,
,,,
,,
,,


,,
,,
,,,
,,,

,,

,,,
,,
,,


,,
,,
,,,
,,
,,
,,

,,,

,,

,,
,,
,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
Logarithmi.
,,
,,
,,

,,,

,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
,,
,,,
,,,
Num.
absolu.

,,
,,

Logarithmi.
,,

,,,
,,

64
Briggs’ 1624 table of logarithms (reconstruction, D. Roegel, 2010)
Chilias quarta.
Num.
absolu.

Logarithmi.
,,,
Num.
absolu.

,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,
,,
,,,

,,,

,,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,,
,,,

,,


,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,


,,
,,
,,
,,,
,,,
,,
,,

,,,

,,
,,,

,,
,,

,,,
,,
,,
,,,

,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,
,,,
,,,

,,


,,
,,
,,
,,,
,,,
,,
,,


,,
,,
,,,
,,,

,,

,,,
,,
,,


,,
,,
,,,
,,
,,
,,

,,,

,,

,,
,,
,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
Logarithmi.
,,
,,
,,

,,,

,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
,,
,,,
,,,
Num.
absolu.

,,
,,

Logarithmi.
,,

,,,
,,

65
Briggs’ 1624 table of logarithms (reconstruction, D. Roegel, 2010)
Chilias quarta.
Num.
absolu.

Logarithmi.
,,,
Num.
absolu.

,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,
,,
,,,

,,,

,,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,,
,,,

,,


,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,


,,
,,
,,
,,,
,,,
,,
,,

,,,

,,
,,,

,,
,,

,,,
,,
,,
,,,

,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,
,,,
,,,

,,


,,
,,
,,
,,,
,,,
,,
,,


,,
,,
,,,
,,,

,,

,,,
,,
,,


,,
,,
,,,
,,
,,
,,

,,,

,,

,,
,,
,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
Logarithmi.
,,
,,
,,

,,,

,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
,,
,,,
,,,
Num.
absolu.

,,
,,

Logarithmi.
,,

,,,
,,

66
Briggs’ 1624 table of logarithms (reconstruction, D. Roegel, 2010)
Chilias quarta.
Num.
absolu.

Logarithmi.
,,,
Num.
absolu.

,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,
,,
,,,

,,,

,,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,,
,,,

,,


,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,


,,
,,
,,
,,,
,,,
,,
,,

,,,

,,
,,,

,,
,,

,,,
,,
,,
,,,

,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,
,,,
,,,

,,


,,
,,
,,
,,,
,,,
,,
,,


,,
,,
,,,
,,,

,,

,,,
,,
,,


,,
,,
,,,
,,
,,
,,

,,,

,,

,,
,,
,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
Logarithmi.
,,
,,
,,

,,,

,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
,,
,,,
,,,
Num.
absolu.

,,
,,

Logarithmi.
,,

,,,
,,

67
Briggs’ 1624 table of logarithms (reconstruction, D. Roegel, 2010)
Chilias quarta.
Num.
absolu.

Logarithmi.
,,,
Num.
absolu.

,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,
,,
,,,

,,,

,,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,,
,,,

,,


,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,


,,
,,
,,
,,,
,,,
,,
,,

,,,

,,
,,,

,,
,,

,,,
,,
,,
,,,

,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,
,,,
,,,

,,


,,
,,
,,
,,,
,,,
,,
,,


,,
,,
,,,
,,,

,,

,,,
,,
,,


,,
,,
,,,
,,
,,
,,

,,,

,,

,,
,,
,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
Logarithmi.
,,
,,
,,

,,,

,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
,,
,,,
,,,
Num.
absolu.

,,
,,

Logarithmi.
,,

,,,
,,

68
Briggs’ 1624 table of logarithms (reconstruction, D. Roegel, 2010)
Chilias quarta.
Num.
absolu.

Logarithmi.
,,,
Num.
absolu.

,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,
,,
,,,

,,,

,,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,,
,,,

,,


,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,


,,
,,
,,
,,,
,,,
,,
,,

,,,

,,
,,,

,,
,,

,,,
,,
,,
,,,

,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,
,,,
,,,

,,


,,
,,
,,
,,,
,,,
,,
,,


,,
,,
,,,
,,,

,,

,,,
,,
,,


,,
,,
,,,
,,
,,
,,

,,,

,,

,,
,,
,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
Logarithmi.
,,
,,
,,

,,,

,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
,,
,,,
,,,
Num.
absolu.

,,
,,

Logarithmi.
,,

,,,
,,

69
Briggs’ 1624 table of logarithms (reconstruction, D. Roegel, 2010)
Chilias quarta.
Num.
absolu.

Logarithmi.
,,,
Num.
absolu.

,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,
,,
,,,

,,,

,,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,,
,,,

,,


,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,


,,
,,
,,
,,,
,,,
,,
,,

,,,

,,
,,,

,,
,,

,,,
,,
,,
,,,

,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,
,,,
,,,

,,


,,
,,
,,
,,,
,,,
,,
,,


,,
,,
,,,
,,,

,,

,,,
,,
,,


,,
,,
,,,
,,
,,
,,

,,,

,,

,,
,,
,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
Logarithmi.
,,
,,
,,

,,,

,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
,,
,,,
,,,
Num.
absolu.

,,
,,

Logarithmi.
,,

,,,
,,

70
Briggs’ 1624 table of logarithms (reconstruction, D. Roegel, 2010)
Chilias quarta.
Num.
absolu.

Logarithmi.
,,,
Num.
absolu.

,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,
,,
,,,

,,,

,,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,,
,,,

,,


,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,


,,
,,
,,
,,,
,,,
,,
,,

,,,

,,
,,,

,,
,,

,,,
,,
,,
,,,

,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,
,,,
,,,

,,


,,
,,
,,
,,,
,,,
,,
,,


,,
,,
,,,
,,,

,,

,,,
,,
,,


,,
,,
,,,
,,
,,
,,

,,,

,,

,,
,,
,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
Logarithmi.
,,
,,
,,

,,,

,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
,,
,,,
,,,
Num.
absolu.

,,
,,

Logarithmi.
,,

,,,
,,

71
Briggs’ 1624 table of logarithms (reconstruction, D. Roegel, 2010)
Chilias quarta.
Num.
absolu.

Logarithmi.
,,,
Num.
absolu.

,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,
,,
,,,

,,,

,,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,,
,,,

,,


,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,


,,
,,
,,
,,,
,,,
,,
,,

,,,

,,
,,,

,,
,,

,,,
,,
,,
,,,

,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,
,,,
,,,

,,


,,
,,
,,
,,,
,,,
,,
,,


,,
,,
,,,
,,,

,,

,,,
,,
,,


,,
,,
,,,
,,
,,
,,

,,,

,,

,,
,,
,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
Logarithmi.
,,
,,
,,

,,,

,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
,,
,,,
,,,
Num.
absolu.

,,
,,

Logarithmi.
,,

,,,
,,

72
Briggs’ 1624 table of logarithms (reconstruction, D. Roegel, 2010)
Chilias quarta.
Num.
absolu.

Logarithmi.
,,,
Num.
absolu.

,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,
,,
,,,

,,,

,,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,,
,,,

,,


,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,


,,
,,
,,
,,,
,,,
,,
,,

,,,

,,
,,,

,,
,,

,,,
,,
,,
,,,

,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,
,,,
,,,

,,


,,
,,
,,
,,,
,,,
,,
,,


,,
,,
,,,
,,,

,,

,,,
,,
,,


,,
,,
,,,
,,
,,
,,

,,,

,,

,,
,,
,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
Logarithmi.
,,
,,
,,

,,,

,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
,,
,,,
,,,
Num.
absolu.

,,
,,

Logarithmi.
,,

,,,
,,

73
Briggs’ 1624 table of logarithms (reconstruction, D. Roegel, 2010)
Chilias quarta.
Num.
absolu.

Logarithmi.
,,,
Num.
absolu.

,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,
,,
,,,

,,,

,,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,,
,,,

,,


,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,


,,
,,
,,
,,,
,,,
,,
,,

,,,

,,
,,,

,,
,,

,,,
,,
,,
,,,

,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,
,,,
,,,

,,


,,
,,
,,
,,,
,,,
,,
,,


,,
,,
,,,
,,,

,,

,,,
,,
,,


,,
,,
,,,
,,
,,
,,

,,,

,,

,,
,,
,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
Logarithmi.
,,
,,
,,

,,,

,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
,,
,,,
,,,
Num.
absolu.

,,
,,

Logarithmi.
,,

,,,
,,

74
Briggs’ 1624 table of logarithms (reconstruction, D. Roegel, 2010)
Chilias quinta.
Num.
absolu.

Logarithmi.
,,,
Num.
absolu.

,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,
,,
,,,

,,,

,,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,,
,,,

,,


,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,


,,
,,
,,
,,,
,,,
,,
,,

,,,

,,
,,,

,,
,,

,,,
,,
,,
,,,

,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,
,,,
,,,

,,


,,
,,
,,
,,,
,,,
,,
,,


,,
,,
,,,
,,,

,,

,,,
,,
,,


,,
,,
,,,
,,
,,
,,

,,,

,,

,,
,,
,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
Logarithmi.
,,
,,
,,

,,,

,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
,,
,,,
,,,
Num.
absolu.

,,
,,

Logarithmi.
,,

,,,
,,

75
Briggs’ 1624 table of logarithms (reconstruction, D. Roegel, 2010)
Chilias quinta.
Num.
absolu.

Logarithmi.
,,,
Num.
absolu.

,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,
,,
,,,

,,,

,,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,,
,,,

,,


,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,


,,
,,
,,
,,,
,,,
,,
,,

,,,

,,
,,,

,,
,,

,,,
,,
,,
,,,

,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,
,,,
,,,

,,


,,
,,
,,
,,,
,,,
,,
,,


,,
,,
,,,
,,,

,,

,,,
,,
,,


,,
,,
,,,
,,
,,
,,

,,,

,,

,,
,,
,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
Logarithmi.
,,
,,
,,

,,,

,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
,,
,,,
,,,
Num.
absolu.

,,
,,

Logarithmi.
,,

,,,
,,

76
Briggs’ 1624 table of logarithms (reconstruction, D. Roegel, 2010)
Chilias quinta.
Num.
absolu.

Logarithmi.
,,,
Num.
absolu.

,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,
,,
,,,

,,,

,,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,,
,,,

,,


,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,


,,
,,
,,
,,,
,,,
,,
,,

,,,

,,
,,,

,,
,,

,,,
,,
,,
,,,

,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,
,,,
,,,

,,


,,
,,
,,
,,,
,,,
,,
,,


,,
,,
,,,
,,,

,,

,,,
,,
,,


,,
,,
,,,
,,
,,
,,

,,,

,,

,,
,,
,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
Logarithmi.
,,
,,
,,

,,,

,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
,,
,,,
,,,
Num.
absolu.

,,
,,

Logarithmi.
,,

,,,
,,

77
Briggs’ 1624 table of logarithms (reconstruction, D. Roegel, 2010)
Chilias quinta.
Num.
absolu.

Logarithmi.
,,,
Num.
absolu.

,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,
,,
,,
,,

,,,

,,,

,,,
,,
,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,,
,,,
,,
,,


,,
,,
,,

,,,
,,
,,
,,,

,,
,,

,,,
,,
,,


,,
,,
,,,
,,
,,
,,

,,
,,
,,
,,,
,,,
,,
,,


,,
,,
,,
,,,
,,,
,,
,,


,,
,,
,,,
,,,
,,
,,


,,
,,
,,,
,,
,,
,,

,,
,,
,,
,,,
,,,
,,
,,


,,
,,
,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
,,
,,,

,,
,,

,,
,,
,,

,,
,,
,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
,,
Logarithmi.
,,
,,
,,

,,,

,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
,,
,,,
,,,
Num.
absolu.

,,
,,

Logarithmi.
,,

,,,
,,

78
Briggs’ 1624 table of logarithms (reconstruction, D. Roegel, 2010)
Chilias quinta.
Num.
absolu.

Logarithmi.
,,,
Num.
absolu.

Logarithmi.
,,,
,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,
,,
,,
,,

,,,

,,,

,,,
,,
,,
,,

,,,

,,,

,,,
,,
,,
,,
,,,
,,
,,
,,

,,
,,
,,

,,,
,,
,,
,,,

,,
,,
,,

,,,
,,
,,


,,
,,
,,,
,,,
,,
,,


,,
,,
,,,
,,
,,
,,

,,
,,
,,
,,,
,,,
,,
,,


,,
,,
,,
,,,
,,,
,,
,,


,,
,,
,,,
,,,
,,
,,


,,
,,
,,,
,,
,,
,,

,,
,,
,,
,,,
,,,
,,
,,


,,
,,
,,

,,,
,,
,,
,,,

,,
,,

,,,
,,
,,


,,
,,
,,,
,,
,,
,,

,,
,,
,,

,,,
,,
,,
,,,

,,
,,

,,,
,,
,,
Logarithmi.
,,
,,
,,

,,,
,,
,,


,,
,,
,,,
,,,
,,
,,

Num.
absolu.

,,

,,,
,,

79
Briggs’ 1624 table of logarithms (reconstruction, D. Roegel, 2010)
Chilias quinta.
Num.
absolu.

Logarithmi.
,,,
Num.
absolu.

Logarithmi.
,,,
,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,
,,
,,
,,

,,,

,,,

,,,
,,
,,
,,

,,,

,,,

,,,
,,
,,
,,
,,,
,,
,,
,,

,,
,,
,,

,,,
,,
,,
,,,

,,
,,
,,

,,,
,,
,,


,,
,,
,,,
,,,
,,
,,


,,
,,
,,,
,,
,,
,,

,,
,,
,,
,,,
,,,
,,
,,


,,
,,
,,
,,,
,,,
,,
,,


,,
,,
,,,
,,,
,,
,,


,,
,,
,,,
,,
,,
,,

,,
,,
,,
,,,
,,,
,,
,,


,,
,,
,,

,,,
,,
,,
,,,

,,
,,

,,,
,,
,,


,,
,,
,,,
,,
,,
,,

,,
,,
,,

,,,
,,
,,
,,,

,,
,,

,,,
,,
,,
Logarithmi.
,,
,,
,,

,,,
,,
,,


,,
,,
,,,
,,,
,,
,,

Num.
absolu.

,,

,,,
,,

80
Briggs’ 1624 table of logarithms (reconstruction, D. Roegel, 2010)
Chilias quinta.
Num.
absolu.

Logarithmi.
,,,
Num.
absolu.

Logarithmi.
,,,
,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,
,,
,,
,,

,,,

,,,

,,,
,,
,,
,,

,,,

,,,

,,,
,,
,,
,,
,,,
,,
,,
,,

,,
,,
,,

,,,
,,
,,
,,,

,,
,,
,,

,,,
,,
,,


,,
,,
,,,
,,,
,,
,,


,,
,,
,,,
,,
,,
,,

,,
,,
,,
,,,
,,,
,,
,,


,,
,,
,,
,,,
,,,
,,
,,


,,
,,
,,,
,,,
,,
,,


,,
,,
,,,
,,
,,
,,

,,
,,
,,
,,,
,,,
,,
,,


,,
,,
,,

,,,
,,
,,
,,,

,,
,,

,,,
,,
,,


,,
,,
,,,
,,
,,
,,

,,
,,
,,

,,,
,,
,,
,,,

,,
,,

,,,
,,
,,
Logarithmi.
,,
,,
,,

,,,
,,
,,


,,
,,
,,,
,,,
,,
,,

Num.
absolu.

,,

,,,
,,

81
Briggs’ 1624 table of logarithms (reconstruction, D. Roegel, 2010)
Chilias quinta.
Num.
absolu.

Logarithmi.
,,,
Num.
absolu.

Logarithmi.
,,,
,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,
,,
,,
,,

,,,

,,,

,,,
,,
,,
,,

,,,

,,,

,,,
,,
,,
,,
,,,
,,
,,
,,

,,
,,
,,

,,,
,,
,,
,,,

,,
,,
,,

,,,
,,
,,


,,
,,
,,,
,,,
,,
,,


,,
,,
,,,
,,
,,
,,

,,
,,
,,
,,,
,,,
,,
,,


,,
,,
,,
,,,
,,,
,,
,,


,,
,,
,,,
,,,
,,
,,


,,
,,
,,,
,,
,,
,,

,,
,,
,,
,,,
,,,
,,
,,


,,
,,
,,

,,,
,,
,,
,,,

,,
,,

,,,
,,
,,


,,
,,
,,,
,,
,,
,,

,,
,,
,,

,,,
,,
,,
,,,

,,
,,

,,,
,,
,,
Logarithmi.
,,
,,
,,

,,,
,,
,,


,,
,,
,,,
,,,
,,
,,

Num.
absolu.

,,

,,,
,,

82
Briggs’ 1624 table of logarithms (reconstruction, D. Roegel, 2010)
Chilias quinta.
Num.
absolu.

Logarithmi.
,,,
Num.
absolu.

Logarithmi.
,,,
,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,
,,
,,
,,

,,,

,,,

,,,
,,
,,
,,

,,,

,,,

,,,
,,
,,
,,
,,,
,,
,,
,,

,,
,,
,,

,,,
,,
,,
,,,

,,
,,
,,

,,,
,,
,,


,,
,,
,,,
,,,
,,
,,


,,
,,
,,,
,,
,,
,,

,,
,,
,,
,,,
,,,
,,
,,


,,
,,
,,
,,,
,,,
,,
,,


,,
,,
,,,
,,,
,,
,,


,,
,,
,,,
,,
,,
,,

,,
,,
,,
,,,
,,,
,,
,,


,,
,,
,,

,,,
,,
,,
,,,

,,
,,

,,,
,,
,,


,,
,,
,,,
,,
,,
,,

,,
,,
,,

,,,
,,
,,
,,,

,,
,,

,,,
,,
,,
Logarithmi.
,,
,,
,,

,,,
,,
,,


,,
,,
,,,
,,,
,,
,,

Num.
absolu.

,,

,,,
,,

83
Briggs’ 1624 table of logarithms (reconstruction, D. Roegel, 2010)
Chilias quinta.
Num.
absolu.

Logarithmi.
,,,
Num.
absolu.

Logarithmi.
,,,
,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,
,,
,,
,,

,,,

,,,

,,,
,,
,,
,,

,,,

,,,

,,,
,,
,,
,,
,,,
,,
,,
,,

,,
,,
,,

,,,
,,
,,
,,,

,,
,,
,,

,,,
,,
,,


,,
,,
,,,
,,,
,,
,,


,,
,,
,,,
,,
,,
,,

,,
,,
,,
,,,
,,,
,,
,,


,,
,,
,,
,,,
,,,
,,
,,


,,
,,
,,,
,,,
,,
,,


,,
,,
,,,
,,
,,
,,

,,
,,
,,
,,,
,,,
,,
,,


,,
,,
,,

,,,
,,
,,
,,,

,,
,,

,,,
,,
,,


,,
,,
,,,
,,
,,
,,

,,
,,
,,

,,,
,,
,,
,,,

,,
,,

,,,
,,
,,
Logarithmi.
,,
,,
,,

,,,
,,
,,


,,
,,
,,,
,,,
,,
,,

Num.
absolu.

,,

,,,
,,

84
Briggs’ 1624 table of logarithms (reconstruction, D. Roegel, 2010)
Chilias sexta.
Num.
absolu.

Logarithmi.
,,,
Num.
absolu.

Logarithmi.
,,,
,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,
,,
,,
,,

,,,

,,,

,,,
,,
,,
,,

,,,

,,,

,,,
,,
,,
,,
,,,
,,
,,
,,

,,
,,
,,

,,,
,,
,,
,,,

,,
,,
,,

,,,
,,
,,


,,
,,
,,,
,,,
,,
,,


,,
,,
,,,
,,
,,
,,

,,
,,
,,
,,,
,,,
,,
,,


,,
,,
,,
,,,
,,,
,,
,,


,,
,,
,,,
,,,
,,
,,


,,
,,
,,,
,,
,,
,,

,,
,,
,,
,,,
,,,
,,
,,


,,
,,
,,

,,,
,,
,,
,,,

,,
,,

,,,
,,
,,


,,
,,
,,,
,,
,,
,,

,,
,,
,,

,,,
,,
,,
,,,

,,
,,

,,,
,,
,,
Logarithmi.
,,
,,
,,

,,,
,,
,,


,,
,,
,,,
,,,
,,
,,

Num.
absolu.

,,

,,,
,,

85
Briggs’ 1624 table of logarithms (reconstruction, D. Roegel, 2010)
Chilias sexta.
Num.
absolu.

Logarithmi.
,,,
Num.
absolu.

Logarithmi.
,,,
,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,
,,
,,
,,

,,,

,,,

,,,
,,
,,
,,

,,,

,,,

,,,
,,
,,
,,
,,,
,,
,,
,,

,,
,,
,,

,,,
,,
,,
,,,

,,
,,
,,

,,,
,,
,,


,,
,,
,,,
,,,
,,
,,


,,
,,
,,,
,,
,,
,,

,,
,,
,,
,,,
,,,
,,
,,


,,
,,
,,
,,,
,,,
,,
,,


,,
,,
,,,
,,,
,,
,,


,,
,,
,,,
,,
,,
,,

,,
,,
,,
,,,
,,,
,,
,,


,,
,,
,,

,,,
,,
,,
,,,

,,
,,

,,,
,,
,,


,,
,,
,,,
,,
,,
,,

,,
,,
,,

,,,
,,
,,
,,,

,,
,,

,,,
,,
,,
Logarithmi.
,,
,,
,,

,,,
,,
,,


,,
,,
,,,
,,,
,,
,,

Num.
absolu.

,,

,,,
,,

86
Briggs’ 1624 table of logarithms (reconstruction, D. Roegel, 2010)
Chilias sexta.
Num.
absolu.

Logarithmi.
,,,
Num.
absolu.

Logarithmi.
,,,
,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,
,,
,,
,,

,,,

,,,

,,,
,,
,,
,,

,,,

,,,

,,,
,,
,,
,,
,,,
,,
,,
,,

,,
,,
,,

,,,
,,
,,
,,,

,,
,,
,,

,,,
,,
,,


,,
,,
,,,
,,,
,,
,,


,,
,,
,,,
,,
,,
,,

,,
,,
,,
,,,
,,,
,,
,,


,,
,,
,,
,,,
,,,
,,
,,


,,
,,
,,,
,,,
,,
,,


,,
,,
,,,
,,
,,
,,

,,
,,
,,
,,,
,,,
,,
,,


,,
,,
,,

,,,
,,
,,
,,,

,,
,,

,,,
,,
,,


,,
,,
,,,
,,
,,
,,

,,
,,
,,

,,,
,,
,,
,,,

,,
,,

,,,
,,
,,
Logarithmi.
,,
,,
,,

,,,
,,
,,


,,
,,
,,,
,,,
,,
,,

Num.
absolu.

,,

,,,
,,

87
Briggs’ 1624 table of logarithms (reconstruction, D. Roegel, 2010)
Chilias sexta.
Num.
absolu.

Logarithmi.
,,,
Num.
absolu.

Logarithmi.
,,,
,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,
,,
,,
,,

,,,

,,,

,,,
,,
,,
,,

,,,

,,,

,,,
,,
,,
,,
,,,
,,
,,
,,

,,
,,
,,

,,,
,,
,,
,,,

,,
,,
,,

,,,
,,
,,


,,
,,
,,,
,,,
,,
,,


,,
,,
,,,
,,
,,
,,

,,
,,
,,
,,,
,,,
,,
,,


,,
,,
,,
,,,
,,,
,,
,,


,,
,,
,,,
,,,
,,
,,


,,
,,
,,,
,,
,,
,,

,,
,,
,,
,,,
,,,
,,
,,


,,
,,
,,

,,,
,,
,,
,,,

,,
,,

,,,
,,
,,


,,
,,
,,,
,,
,,
,,

,,
,,
,,

,,,
,,
,,
,,,

,,
,,

,,,
,,
,,
Logarithmi.
,,
,,
,,

,,,
,,
,,


,,
,,
,,,
,,,
,,
,,

Num.
absolu.

,,

,,,
,,

88
Briggs’ 1624 table of logarithms (reconstruction, D. Roegel, 2010)
Chilias sexta.
Num.
absolu.

Logarithmi.
,,,
Num.
absolu.

Logarithmi.
,,,
,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,
,,
,,
,,

,,,

,,,

,,,
,,
,,
,,

,,,

,,,

,,,
,,
,,
,,
,,,
,,
,,
,,

,,
,,
,,

,,,
,,
,,
,,,

,,
,,
,,

,,,
,,
,,


,,
,,
,,,
,,,
,,
,,


,,
,,
,,,
,,
,,
,,

,,
,,
,,
,,,
,,,
,,
,,


,,
,,
,,
,,,
,,,
,,
,,


,,
,,
,,,
,,,
,,
,,


,,
,,
,,,
,,
,,
,,

,,
,,
,,
,,,
,,,
,,
,,


,,
,,
,,

,,,
,,
,,
,,,

,,
,,

,,,
,,
,,


,,
,,
,,,
,,
,,
,,

,,
,,
,,

,,,
,,
,,
,,,

,,
,,

,,,
,,
,,
Logarithmi.
,,
,,
,,

,,,
,,
,,


,,
,,
,,,
,,,
,,
,,

Num.
absolu.

,,

,,,
,,

89
Briggs’ 1624 table of logarithms (reconstruction, D. Roegel, 2010)
Chilias sexta.
Num.
absolu.

Logarithmi.
,,,
Num.
absolu.

Logarithmi.
,,,
,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,
,,
,,
,,

,,,

,,,

,,,
,,
,,
,,

,,,

,,,

,,,
,,
,,
,,
,,,
,,
,,
,,

,,
,,
,,

,,,
,,
,,
,,,

,,
,,
,,

,,,
,,
,,


,,
,,
,,,
,,,
,,
,,


,,
,,
,,,
,,
,,
,,

,,
,,
,,
,,,
,,,
,,
,,


,,
,,
,,
,,,
,,,
,,
,,


,,
,,
,,,
,,,
,,
,,


,,
,,
,,,
,,
,,
,,

,,
,,
,,
,,,
,,,
,,
,,


,,
,,
,,

,,,
,,
,,
,,,

,,
,,

,,,
,,
,,


,,
,,
,,,
,,
,,
,,

,,
,,
,,

,,,
,,
,,
,,,

,,
,,

,,,
,,
,,
Logarithmi.
,,
,,
,,

,,,
,,
,,


,,
,,
,,,
,,,
,,
,,

Num.
absolu.

,,

,,,
,,

90
Briggs’ 1624 table of logarithms (reconstruction, D. Roegel, 2010)
Chilias sexta.
Num.
absolu.

Logarithmi.
,,,
Num.
absolu.

Logarithmi.
,,,
,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,
,,
,,
,,

,,,

,,,

,,,
,,
,,
,,

,,,

,,,

,,,
,,
,,
,,
,,,
,,
,,
,,

,,
,,
,,

,,,
,,
,,
,,,

,,
,,
,,

,,,
,,
,,


,,
,,
,,,
,,,
,,
,,


,,
,,
,,,
,,
,,
,,

,,
,,
,,
,,,
,,,
,,
,,


,,
,,
,,
,,,
,,,
,,
,,


,,
,,
,,,
,,,
,,
,,


,,
,,
,,,
,,
,,
,,

,,
,,
,,
,,,
,,,
,,
,,


,,
,,
,,

,,,
,,
,,
,,,

,,
,,

,,,
,,
,,


,,
,,
,,,
,,
,,
,,

,,
,,
,,

,,,
,,
,,
,,,

,,
,,

,,,
,,
,,
Logarithmi.
,,
,,
,,

,,,
,,
,,


,,
,,
,,,
,,,
,,
,,

Num.
absolu.

,,

,,,
,,

91
Briggs’ 1624 table of logarithms (reconstruction, D. Roegel, 2010)
Chilias sexta.
Num.
absolu.

Logarithmi.
,,,
Num.
absolu.

Logarithmi.
,,,
,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,
,,
,,
,,

,,,

,,,

,,,
,,
,,
,,

,,,

,,,

,,,
,,
,,
,,
,,,
,,
,,
,,

,,
,,
,,

,,,
,,
,,
,,,

,,
,,
,,

,,,
,,
,,


,,
,,
,,,
,,,
,,
,,


,,
,,
,,,
,,
,,
,,

,,
,,
,,
,,,
,,,
,,
,,


,,
,,
,,
,,,
,,,
,,
,,


,,
,,
,,,
,,,
,,
,,


,,
,,
,,,
,,
,,
,,

,,
,,
,,
,,,
,,,
,,
,,


,,
,,
,,

,,,
,,
,,
,,,

,,
,,

,,,
,,
,,


,,
,,
,,,
,,
,,
,,

,,
,,
,,

,,,
,,
,,
,,,

,,
,,

,,,
,,
,,
Logarithmi.
,,
,,
,,

,,,
,,
,,


,,
,,
,,,
,,,
,,
,,

Num.
absolu.

,,

,,,
,,

92
Briggs’ 1624 table of logarithms (reconstruction, D. Roegel, 2010)
Chilias sexta.
Num.
absolu.

Logarithmi.
,,,
Num.
absolu.

Logarithmi.
,,,
,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,
,,
,,
,,

,,,

,,,

,,,
,,
,,
,,

,,,

,,,

,,,
,,
,,
,,
,,,
,,
,,
,,

,,
,,
,,

,,,
,,
,,
,,,

,,
,,
,,

,,,
,,
,,


,,
,,
,,,
,,,
,,
,,


,,
,,
,,,
,,
,,
,,

,,
,,
,,
,,,
,,,
,,
,,


,,
,,
,,
,,,
,,,
,,
,,


,,
,,
,,,
,,,
,,
,,


,,
,,
,,,
,,
,,
,,

,,
,,
,,
,,,
,,,
,,
,,


,,
,,
,,

,,,
,,
,,
,,,

,,
,,

,,,
,,
,,


,,
,,
,,,
,,
,,
,,

,,
,,
,,

,,,
,,
,,
,,,

,,
,,

,,,
,,
,,
Logarithmi.
,,
,,
,,

,,,
,,
,,


,,
,,
,,,
,,,
,,
,,

Num.
absolu.

,,

,,,
,,

93
Briggs’ 1624 table of logarithms (reconstruction, D. Roegel, 2010)
Chilias sexta.
Num.
absolu.

Logarithmi.
,,,
Num.
absolu.

Logarithmi.
,,,
,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,
,,
,,
,,

,,,

,,,

,,,
,,
,,
,,

,,,

,,,

,,,
,,
,,
,,
,,,
,,
,,
,,

,,
,,
,,

,,,
,,
,,
,,,

,,
,,
,,

,,,
,,
,,


,,
,,
,,,
,,,
,,
,,


,,
,,
,,,
,,
,,
,,

,,
,,
,,
,,,
,,,
,,
,,


,,
,,
,,
,,,
,,,
,,
,,


,,
,,
,,,
,,,
,,
,,


,,
,,
,,,
,,
,,
,,

,,
,,
,,
,,,
,,,
,,
,,


,,
,,
,,

,,,
,,
,,
,,,

,,
,,

,,,
,,
,,


,,
,,
,,,
,,
,,
,,

,,
,,
,,

,,,
,,
,,
,,,

,,
,,

,,,
,,
,,
Logarithmi.
,,
,,
,,

,,,
,,
,,


,,
,,
,,,
,,,
,,
,,

Num.
absolu.

,,

,,,
,,

94
Briggs’ 1624 table of logarithms (reconstruction, D. Roegel, 2010)
Chilias septima.
Num.
absolu.

Logarithmi.
,,,
Num.
absolu.

Logarithmi.
,,,
,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,
,,
,,
,,

,,,

,,,

,,,
,,
,,
,,

,,,

,,,

,,,
,,
,,
,,
,,,
,,
,,
,,

,,
,,
,,

,,,
,,
,,
,,,

,,
,,
,,

,,,
,,
,,


,,
,,
,,,
,,,
,,
,,


,,
,,
,,,
,,
,,
,,

,,
,,
,,
,,,
,,,
,,
,,


,,
,,
,,
,,,
,,,
,,
,,


,,
,,
,,,
,,,
,,
,,


,,
,,
,,,
,,
,,
,,

,,
,,
,,
,,,
,,,
,,
,,


,,
,,
,,

,,,
,,
,,
,,,

,,
,,

,,,
,,
,,


,,
,,
,,,
,,
,,
,,

,,
,,
,,

,,,
,,
,,
,,,

,,
,,

,,,
,,
,,
Logarithmi.
,,
,,
,,

,,,
,,
,,


,,
,,
,,,
,,,
,,
,,

Num.
absolu.

,,

,,,
,,

95
Briggs’ 1624 table of logarithms (reconstruction, D. Roegel, 2010)
Chilias septima.
Num.
absolu.

Logarithmi.
,,,
Num.
absolu.

Logarithmi.
,,,
,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,
,,
,,
,,

,,,

,,,

,,,
,,
,,
,,

,,,

,,,

,,,
,,
,,
,,
,,,
,,
,,
,,

,,
,,
,,

,,,
,,
,,
,,,

,,
,,
,,

,,,
,,
,,


,,
,,
,,,
,,,
,,
,,


,,
,,
,,,
,,
,,
,,

,,
,,
,,
,,,
,,,
,,
,,


,,
,,
,,
,,,
,,,
,,
,,


,,
,,
,,,
,,,
,,
,,


,,
,,
,,,
,,
,,
,,

,,
,,
,,
,,,
,,,
,,
,,


,,
,,
,,

,,,
,,
,,
,,,

,,
,,

,,,
,,
,,


,,
,,
,,,
,,
,,
,,

,,
,,
,,

,,,
,,
,,
,,,

,,
,,

,,,
,,
,,
Logarithmi.
,,
,,
,,

,,,
,,
,,


,,
,,
,,,
,,,
,,
,,

Num.
absolu.

,,

,,,
,,

96
Briggs’ 1624 table of logarithms (reconstruction, D. Roegel, 2010)
Chilias septima.
Num.
absolu.

Logarithmi.
,,,
Num.
absolu.

Logarithmi.
,,,
,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,
,,
,,
,,

,,,

,,,

,,,
,,
,,
,,

,,,

,,,

,,,
,,
,,
,,
,,,
,,
,,
,,

,,
,,
,,

,,,
,,
,,
,,,

,,
,,
,,

,,,
,,
,,


,,
,,
,,,
,,,
,,
,,


,,
,,
,,,
,,
,,
,,

,,
,,
,,
,,,
,,,
,,
,,


,,
,,
,,
,,,
,,,
,,
,,


,,
,,
,,,
,,,
,,
,,


,,
,,
,,,
,,
,,
,,

,,
,,
,,
,,,
,,,
,,
,,


,,
,,
,,

,,,
,,
,,
,,,

,,
,,

,,,
,,
,,


,,
,,
,,,
,,
,,
,,

,,
,,
,,

,,,
,,
,,
,,,

,,
,,

,,,
,,
,,
Logarithmi.
,,
,,
,,

,,,
,,
,,


,,
,,
,,,
,,,
,,
,,

Num.
absolu.

,,

,,,
,,

97
Briggs’ 1624 table of logarithms (reconstruction, D. Roegel, 2010)
Chilias septima.
Num.
absolu.

Logarithmi.
,,,
Num.
absolu.

Logarithmi.
,,,
,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,
,,
,,
,,

,,,

,,,

,,,
,,
,,
,,

,,,

,,,

,,,
,,
,,
,,
,,,
,,
,,
,,

,,
,,
,,

,,,
,,
,,
,,,

,,
,,
,,

,,,
,,
,,


,,
,,
,,,
,,,
,,
,,


,,
,,
,,,
,,
,,
,,

,,
,,
,,
,,,
,,,
,,
,,


,,
,,
,,
,,,
,,,
,,
,,


,,
,,
,,,
,,,
,,
,,


,,
,,
,,,
,,
,,
,,

,,
,,
,,
,,,
,,,
,,
,,


,,
,,
,,

,,,
,,
,,
,,,

,,
,,

,,,
,,
,,


,,
,,
,,,
,,
,,
,,

,,
,,
,,

,,,
,,
,,
,,,

,,
,,

,,,
,,
,,
Logarithmi.
,,
,,
,,

,,,
,,
,,


,,
,,
,,,
,,,
,,
,,

Num.
absolu.

,,

,,,
,,

98
Briggs’ 1624 table of logarithms (reconstruction, D. Roegel, 2010)
Chilias septima.
Num.
absolu.

Logarithmi.
,,,
Num.
absolu.

Logarithmi.
,,,
,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,
,,
,,
,,

,,,

,,,

,,,
,,
,,
,,

,,,

,,,

,,,
,,
,,
,,
,,,
,,
,,
,,

,,
,,
,,

,,,
,,
,,
,,,

,,
,,
,,

,,,
,,
,,


,,
,,
,,,
,,,
,,
,,


,,
,,
,,,
,,
,,
,,

,,
,,
,,
,,,
,,,
,,
,,


,,
,,
,,
,,,
,,,
,,
,,


,,
,,
,,,
,,,
,,
,,


,,
,,
,,,
,,
,,
,,

,,
,,
,,
,,,
,,,
,,
,,


,,
,,
,,

,,,
,,
,,
,,,

,,
,,

,,,
,,
,,


,,
,,
,,,
,,
,,
,,

,,
,,
,,

,,,
,,
,,
,,,

,,
,,

,,,
,,
,,
Logarithmi.
,,
,,
,,

,,,
,,
,,


,,
,,
,,,
,,,
,,
,,

Num.
absolu.

,,

,,,
,,

99
Briggs’ 1624 table of logarithms (reconstruction, D. Roegel, 2010)
Chilias septima.
Num.
absolu.

Logarithmi.
,,,
Num.
absolu.

,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,
,,
,,,

,,,

,,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,,
,,,

,,


,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,


,,
,,
,,
,,,
,,,
,,
,,

,,,

,,
,,,

,,
,,

,,,
,,
,,
,,,

,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,
,,,
,,,

,,


,,
,,
,,
,,,
,,,
,,
,,


,,
,,
,,,
,,,

,,

,,,
,,
,,


,,
,,
,,,
,,
,,
,,

,,,

,,

,,
,,
,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
Logarithmi.
,,
,,
,,

,,,

,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
,,
,,,
,,,
Num.
absolu.

,,
,,

Logarithmi.
,,

,,,
,,

100
Briggs’ 1624 table of logarithms (reconstruction, D. Roegel, 2010)
Chilias septima.
Num.
absolu.

Logarithmi.
,,,
Num.
absolu.

,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,
,,
,,,

,,,

,,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,,
,,,

,,


,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,


,,
,,
,,
,,,
,,,
,,
,,

,,,

,,
,,,

,,
,,

,,,
,,
,,
,,,

,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,
,,,
,,,

,,


,,
,,
,,
,,,
,,,
,,
,,


,,
,,
,,,
,,,

,,

,,,
,,
,,


,,
,,
,,,
,,
,,
,,

,,,

,,

,,
,,
,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
Logarithmi.
,,
,,
,,

,,,

,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
,,
,,,
,,,
Num.
absolu.

,,
,,

Logarithmi.
,,

,,,
,,

101
Briggs’ 1624 table of logarithms (reconstruction, D. Roegel, 2010)
Chilias septima.
Num.
absolu.

Logarithmi.
,,,
Num.
absolu.

,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,
,,
,,,

,,,

,,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,,
,,,

,,


,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,


,,
,,
,,
,,,
,,,
,,
,,

,,,

,,
,,,

,,
,,

,,,
,,
,,
,,,

,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,
,,,
,,,

,,


,,
,,
,,
,,,
,,,
,,
,,


,,
,,
,,,
,,,

,,

,,,
,,
,,


,,
,,
,,,
,,
,,
,,

,,,

,,

,,
,,
,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
Logarithmi.
,,
,,
,,

,,,

,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
,,
,,,
,,,
Num.
absolu.

,,
,,

Logarithmi.
,,

,,,
,,

102
Briggs’ 1624 table of logarithms (reconstruction, D. Roegel, 2010)
Chilias septima.
Num.
absolu.

Logarithmi.
,,,
Num.
absolu.

,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,
,,
,,,

,,,

,,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,,
,,,

,,


,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,


,,
,,
,,
,,,
,,,
,,
,,

,,,

,,
,,,

,,
,,

,,,
,,
,,
,,,

,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,
,,,
,,,

,,


,,
,,
,,
,,,
,,,
,,
,,


,,
,,
,,,
,,,

,,

,,,
,,
,,


,,
,,
,,,
,,
,,
,,

,,,

,,

,,
,,
,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
Logarithmi.
,,
,,
,,

,,,

,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
,,
,,,
,,,
Num.
absolu.

,,
,,

Logarithmi.
,,

,,,
,,

103
Briggs’ 1624 table of logarithms (reconstruction, D. Roegel, 2010)
Chilias septima.
Num.
absolu.

Logarithmi.
,,,
Num.
absolu.

,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,
,,
,,,

,,,

,,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,,
,,,

,,


,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,


,,
,,
,,
,,,
,,,
,,
,,

,,,

,,
,,,

,,
,,

,,,
,,
,,
,,,

,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,
,,,
,,,

,,


,,
,,
,,
,,,
,,,
,,
,,


,,
,,
,,,
,,,

,,

,,,
,,
,,


,,
,,
,,,
,,
,,
,,

,,,

,,

,,
,,
,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
Logarithmi.
,,
,,
,,

,,,

,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
,,
,,,
,,,
Num.
absolu.

,,
,,

Logarithmi.
,,

,,,
,,

104
Briggs’ 1624 table of logarithms (reconstruction, D. Roegel, 2010)
Chilias octaua.
Num.
absolu.

Logarithmi.
,,,
Num.
absolu.

,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,
,,
,,,

,,,

,,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,,
,,,

,,


,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,


,,
,,
,,
,,,
,,,
,,
,,

,,,

,,
,,,

,,
,,

,,,
,,
,,
,,,

,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,
,,,
,,,

,,


,,
,,
,,
,,,
,,,
,,
,,


,,
,,
,,,
,,,

,,

,,,
,,
,,


,,
,,
,,,
,,
,,
,,

,,,

,,

,,
,,
,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
Logarithmi.
,,
,,
,,

,,,

,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
,,
,,,
,,,
Num.
absolu.

,,
,,

Logarithmi.
,,

,,,
,,

105
Briggs’ 1624 table of logarithms (reconstruction, D. Roegel, 2010)
Chilias octaua.
Num.
absolu.

Logarithmi.
,,,
Num.
absolu.

,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,
,,
,,,

,,,

,,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,,
,,,

,,


,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,


,,
,,
,,
,,,
,,,
,,
,,

,,,

,,
,,,

,,
,,

,,,
,,
,,
,,,

,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,
,,,
,,,

,,


,,
,,
,,
,,,
,,,
,,
,,


,,
,,
,,,
,,,

,,

,,,
,,
,,


,,
,,
,,,
,,
,,
,,

,,,

,,

,,
,,
,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
Logarithmi.
,,
,,
,,

,,,

,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
,,
,,,
,,,
Num.
absolu.

,,
,,

Logarithmi.
,,

,,,
,,

106
Briggs’ 1624 table of logarithms (reconstruction, D. Roegel, 2010)
Chilias octaua.
Num.
absolu.

Logarithmi.
,,,
Num.
absolu.

,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,
,,
,,,

,,,

,,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,,
,,,

,,


,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,


,,
,,
,,
,,,
,,,
,,
,,

,,,

,,
,,,

,,
,,

,,,
,,
,,
,,,

,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,
,,,
,,,

,,


,,
,,
,,
,,,
,,,
,,
,,


,,
,,
,,,
,,,

,,

,,,
,,
,,


,,
,,
,,,
,,
,,
,,

,,,

,,

,,
,,
,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
Logarithmi.
,,
,,
,,

,,,

,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
,,
,,,
,,,
Num.
absolu.

,,
,,

Logarithmi.
,,

,,,
,,

107
Briggs’ 1624 table of logarithms (reconstruction, D. Roegel, 2010)
Chilias octaua.
Num.
absolu.

Logarithmi.
,,,
Num.
absolu.

,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,
,,
,,,

,,,

,,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,,
,,,

,,


,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,


,,
,,
,,
,,,
,,,
,,
,,

,,,

,,
,,,

,,
,,

,,,
,,
,,
,,,

,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,
,,,
,,,

,,


,,
,,
,,
,,,
,,,
,,
,,


,,
,,
,,,
,,,

,,

,,,
,,
,,


,,
,,
,,,
,,
,,
,,

,,,

,,

,,
,,
,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
Logarithmi.
,,
,,
,,

,,,

,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
,,
,,,
,,,
Num.
absolu.

,,
,,

Logarithmi.
,,

,,,
,,

108
Briggs’ 1624 table of logarithms (reconstruction, D. Roegel, 2010)
Chilias octaua.
Num.
absolu.

Logarithmi.
,,,
Num.
absolu.

,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,
,,
,,,

,,,

,,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,,
,,,

,,


,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,


,,
,,
,,
,,,
,,,
,,
,,

,,,

,,
,,,

,,
,,

,,,
,,
,,
,,,

,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,
,,,
,,,

,,


,,
,,
,,
,,,
,,,
,,
,,


,,
,,
,,,
,,,

,,

,,,
,,
,,


,,
,,
,,,
,,
,,
,,

,,,

,,

,,
,,
,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
Logarithmi.
,,
,,
,,

,,,

,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
,,
,,,
,,,
Num.
absolu.

,,
,,

Logarithmi.
,,

,,,
,,

109
Briggs’ 1624 table of logarithms (reconstruction, D. Roegel, 2010)
Chilias octaua.
Num.
absolu.

Logarithmi.
,,,
Num.
absolu.

,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,
,,
,,,

,,,

,,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,,
,,,

,,


,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,


,,
,,
,,
,,,
,,,
,,
,,

,,,

,,
,,,

,,
,,

,,,
,,
,,
,,,

,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,
,,,
,,,

,,


,,
,,
,,
,,,
,,,
,,
,,


,,
,,
,,,
,,,

,,

,,,
,,
,,


,,
,,
,,,
,,
,,
,,

,,,

,,

,,
,,
,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
Logarithmi.
,,
,,
,,

,,,

,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
,,
,,,
,,,
Num.
absolu.

,,
,,

Logarithmi.
,,

,,,
,,

110
Briggs’ 1624 table of logarithms (reconstruction, D. Roegel, 2010)
Chilias octaua.
Num.
absolu.

Logarithmi.
,,,
Num.
absolu.

,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,
,,
,,,

,,,

,,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,,
,,,

,,


,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,


,,
,,
,,
,,,
,,,
,,
,,

,,,

,,
,,,

,,
,,

,,,
,,
,,
,,,

,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,
,,,
,,,

,,


,,
,,
,,
,,,
,,,
,,
,,


,,
,,
,,,
,,,

,,

,,,
,,
,,


,,
,,
,,,
,,
,,
,,

,,,

,,

,,
,,
,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
Logarithmi.
,,
,,
,,

,,,

,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
,,
,,,
,,,
Num.
absolu.

,,
,,

Logarithmi.
,,

,,,
,,

111
Briggs’ 1624 table of logarithms (reconstruction, D. Roegel, 2010)
Chilias octaua.
Num.
absolu.

Logarithmi.
,,,
Num.
absolu.

,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,
,,
,,,

,,,

,,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,,
,,,

,,


,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,


,,
,,
,,
,,,
,,,
,,
,,

,,,

,,
,,,

,,
,,

,,,
,,
,,
,,,

,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,
,,,
,,,

,,


,,
,,
,,
,,,
,,,
,,
,,


,,
,,
,,,
,,,

,,

,,,
,,
,,


,,
,,
,,,
,,
,,
,,

,,,

,,

,,
,,
,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
Logarithmi.
,,
,,
,,

,,,

,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
,,
,,,
,,,
Num.
absolu.

,,
,,

Logarithmi.
,,

,,,
,,

112
Briggs’ 1624 table of logarithms (reconstruction, D. Roegel, 2010)
Chilias octaua.
Num.
absolu.

Logarithmi.
,,,
Num.
absolu.

,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,
,,
,,,

,,,

,,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,,
,,,

,,


,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,


,,
,,
,,
,,,
,,,
,,
,,

,,,

,,
,,,

,,
,,

,,,
,,
,,
,,,

,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,
,,,
,,,

,,


,,
,,
,,
,,,
,,,
,,
,,


,,
,,
,,,
,,,

,,

,,,
,,
,,


,,
,,
,,,
,,
,,
,,

,,,

,,

,,
,,
,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
Logarithmi.
,,
,,
,,

,,,

,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
,,
,,,
,,,
Num.
absolu.

,,
,,

Logarithmi.
,,

,,,
,,

113
Briggs’ 1624 table of logarithms (reconstruction, D. Roegel, 2010)
Chilias octaua.
Num.
absolu.

Logarithmi.
,,,
Num.
absolu.

,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,
,,
,,,

,,,

,,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,,
,,,

,,


,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,


,,
,,
,,
,,,
,,,
,,
,,

,,,

,,
,,,

,,
,,

,,,
,,
,,
,,,

,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,
,,,
,,,

,,


,,
,,
,,
,,,
,,,
,,
,,


,,
,,
,,,
,,,

,,

,,,
,,
,,


,,
,,
,,,
,,
,,
,,

,,,

,,

,,
,,
,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
Logarithmi.
,,
,,
,,

,,,

,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
,,
,,,
,,,
Num.
absolu.

,,
,,

Logarithmi.
,,

,,,
,,

114
Briggs’ 1624 table of logarithms (reconstruction, D. Roegel, 2010)
Chilias nona.
Num.
absolu.

Logarithmi.
,,,
Num.
absolu.

,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,
,,
,,,

,,,

,,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,,
,,,

,,


,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,


,,
,,
,,
,,,
,,,
,,
,,

,,,

,,
,,,

,,
,,

,,,
,,
,,
,,,

,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,
,,,
,,,

,,


,,
,,
,,
,,,
,,,
,,
,,


,,
,,
,,,
,,,

,,

,,,
,,
,,


,,
,,
,,,
,,
,,
,,

,,,

,,

,,
,,
,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
Logarithmi.
,,
,,
,,

,,,

,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
,,
,,,
,,,
Num.
absolu.

,,
,,

Logarithmi.
,,

,,,
,,

115
Briggs’ 1624 table of logarithms (reconstruction, D. Roegel, 2010)
Chilias nona.
Num.
absolu.

Logarithmi.
,,,
Num.
absolu.

,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,
,,
,,,

,,,

,,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,,
,,,

,,


,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,


,,
,,
,,
,,,
,,,
,,
,,

,,,

,,
,,,

,,
,,

,,,
,,
,,
,,,

,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,
,,,
,,,

,,


,,
,,
,,
,,,
,,,
,,
,,


,,
,,
,,,
,,,

,,

,,,
,,
,,


,,
,,
,,,
,,
,,
,,

,,,

,,

,,
,,
,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
Logarithmi.
,,
,,
,,

,,,

,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
,,
,,,
,,,
Num.
absolu.

,,
,,

Logarithmi.
,,

,,,
,,

116
Briggs’ 1624 table of logarithms (reconstruction, D. Roegel, 2010)
Chilias nona.
Num.
absolu.

Logarithmi.
,,,
Num.
absolu.

,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,
,,
,,,

,,,

,,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,,
,,,

,,


,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,


,,
,,
,,
,,,
,,,
,,
,,

,,,

,,
,,,

,,
,,

,,,
,,
,,
,,,

,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,
,,,
,,,

,,


,,
,,
,,
,,,
,,,
,,
,,


,,
,,
,,,
,,,

,,

,,,
,,
,,


,,
,,
,,,
,,
,,
,,

,,,

,,

,,
,,
,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
Logarithmi.
,,
,,
,,

,,,

,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
,,
,,,
,,,
Num.
absolu.

,,
,,

Logarithmi.
,,

,,,
,,

117
Briggs’ 1624 table of logarithms (reconstruction, D. Roegel, 2010)
Chilias nona.
Num.
absolu.

Logarithmi.
,,,
Num.
absolu.

,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,
,,
,,,

,,,

,,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,,
,,,

,,


,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,


,,
,,
,,
,,,
,,,
,,
,,

,,,

,,
,,,

,,
,,

,,,
,,
,,
,,,

,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,
,,,
,,,

,,


,,
,,
,,
,,,
,,,
,,
,,


,,
,,
,,,
,,,

,,

,,,
,,
,,


,,
,,
,,,
,,
,,
,,

,,,

,,

,,
,,
,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
Logarithmi.
,,
,,
,,

,,,

,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
,,
,,,
,,,
Num.
absolu.

,,
,,

Logarithmi.
,,

,,,
,,

118
Briggs’ 1624 table of logarithms (reconstruction, D. Roegel, 2010)
Chilias nona.
Num.
absolu.

Logarithmi.
,,,
Num.
absolu.

,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,
,,
,,,

,,,

,,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,,
,,,

,,


,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,


,,
,,
,,
,,,
,,,
,,
,,

,,,

,,
,,,

,,
,,

,,,
,,
,,
,,,

,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,
,,,
,,,

,,


,,
,,
,,
,,,
,,,
,,
,,


,,
,,
,,,
,,,

,,

,,,
,,
,,


,,
,,
,,,
,,
,,
,,

,,,

,,

,,
,,
,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
Logarithmi.
,,
,,
,,

,,,

,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
,,
,,,
,,,
Num.
absolu.

,,
,,

Logarithmi.
,,

,,,
,,

119
Briggs’ 1624 table of logarithms (reconstruction, D. Roegel, 2010)
Chilias nona.
Num.
absolu.

Logarithmi.
,,,
Num.
absolu.

,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,
,,
,,,

,,,

,,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,,
,,,

,,


,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,


,,
,,
,,
,,,
,,,
,,
,,

,,,

,,
,,,

,,
,,

,,,
,,
,,
,,,

,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,
,,,
,,,

,,


,,
,,
,,
,,,
,,,
,,
,,


,,
,,
,,,
,,,

,,

,,,
,,
,,


,,
,,
,,,
,,
,,
,,

,,,

,,

,,
,,
,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
Logarithmi.
,,
,,
,,

,,,

,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
,,
,,,
,,,
Num.
absolu.

,,
,,

Logarithmi.
,,

,,,
,,

120
Briggs’ 1624 table of logarithms (reconstruction, D. Roegel, 2010)
Chilias nona.
Num.
absolu.

Logarithmi.
,,,
Num.
absolu.

,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,
,,
,,,

,,,

,,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,,
,,,

,,


,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,


,,
,,
,,
,,,
,,,
,,
,,

,,,

,,
,,,

,,
,,

,,,
,,
,,
,,,

,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,
,,,
,,,

,,


,,
,,
,,
,,,
,,,
,,
,,


,,
,,
,,,
,,,

,,

,,,
,,
,,


,,
,,
,,,
,,
,,
,,

,,,

,,

,,
,,
,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
Logarithmi.
,,
,,
,,

,,,

,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
,,
,,,
,,,
Num.
absolu.

,,
,,

Logarithmi.
,,

,,,
,,

121
Briggs’ 1624 table of logarithms (reconstruction, D. Roegel, 2010)
Chilias nona.
Num.
absolu.

Logarithmi.
,,,
Num.
absolu.

,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,
,,
,,,

,,,

,,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,,
,,,

,,


,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,


,,
,,
,,
,,,
,,,
,,
,,

,,,

,,
,,,

,,
,,

,,,
,,
,,
,,,

,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,
,,,
,,,

,,


,,
,,
,,
,,,
,,,
,,
,,


,,
,,
,,,
,,,

,,

,,,
,,
,,


,,
,,
,,,
,,
,,
,,

,,,

,,

,,
,,
,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
Logarithmi.
,,
,,
,,

,,,

,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
,,
,,,
,,,
Num.
absolu.

,,
,,

Logarithmi.
,,

,,,
,,

122
Briggs’ 1624 table of logarithms (reconstruction, D. Roegel, 2010)
Chilias nona.
Num.
absolu.

Logarithmi.
,,,
Num.
absolu.

,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,
,,
,,,

,,,

,,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,,
,,,

,,


,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,


,,
,,
,,
,,,
,,,
,,
,,

,,,

,,
,,,

,,
,,

,,,
,,
,,
,,,

,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,
,,,
,,,

,,


,,
,,
,,
,,,
,,,
,,
,,


,,
,,
,,,
,,,

,,

,,,
,,
,,


,,
,,
,,,
,,
,,
,,

,,,

,,

,,
,,
,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
Logarithmi.
,,
,,
,,

,,,

,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
,,
,,,
,,,
Num.
absolu.

,,
,,

Logarithmi.
,,

,,,
,,

123
Briggs’ 1624 table of logarithms (reconstruction, D. Roegel, 2010)
Chilias nona.
Num.
absolu.

Logarithmi.
,,,
Num.
absolu.

,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,
,,
,,,

,,,

,,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,,
,,,

,,


,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,


,,
,,
,,
,,,
,,,
,,
,,

,,,

,,
,,,

,,
,,

,,,
,,
,,
,,,

,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,
,,,
,,,

,,


,,
,,
,,
,,,
,,,
,,
,,


,,
,,
,,,
,,,

,,

,,,
,,
,,


,,
,,
,,,
,,
,,
,,

,,,

,,

,,
,,
,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
Logarithmi.
,,
,,
,,

,,,

,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
,,
,,,
,,,
Num.
absolu.

,,
,,

Logarithmi.
,,

,,,
,,

124
Briggs’ 1624 table of logarithms (reconstruction, D. Roegel, 2010)
Chilias decima.
Num.
absolu.

Logarithmi.
,,,
Num.
absolu.

,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,
,,
,,,

,,,

,,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,,
,,,

,,


,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,


,,
,,
,,
,,,
,,,
,,
,,

,,,

,,
,,,

,,
,,

,,,
,,
,,
,,,

,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,
,,,
,,,

,,


,,
,,
,,
,,,
,,,
,,
,,


,,
,,
,,,
,,,

,,

,,,
,,
,,


,,
,,
,,,
,,
,,
,,

,,,

,,

,,
,,
,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
Logarithmi.
,,
,,
,,

,,,

,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
,,
,,,
,,,
Num.
absolu.

,,
,,

Logarithmi.
,,

,,,
,,

125
Briggs’ 1624 table of logarithms (reconstruction, D. Roegel, 2010)
Chilias decima.
Num.
absolu.

Logarithmi.
,,,
Num.
absolu.

,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,
,,
,,,

,,,

,,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,,
,,,

,,


,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,


,,
,,
,,
,,,
,,,
,,
,,

,,,

,,
,,,

,,
,,

,,,
,,
,,
,,,

,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,
,,,
,,,

,,


,,
,,
,,
,,,
,,,
,,
,,


,,
,,
,,,
,,,

,,

,,,
,,
,,


,,
,,
,,,
,,
,,
,,

,,,

,,

,,
,,
,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
Logarithmi.
,,
,,
,,

,,,

,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
,,
,,,
,,,
Num.
absolu.

,,
,,

Logarithmi.
,,

,,,
,,

126
Briggs’ 1624 table of logarithms (reconstruction, D. Roegel, 2010)
Chilias decima.
Num.
absolu.

Logarithmi.
,,,
Num.
absolu.

,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,
,,
,,,

,,,

,,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,,
,,,

,,


,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,


,,
,,
,,
,,,
,,,
,,
,,

,,,

,,
,,,

,,
,,

,,,
,,
,,
,,,

,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,
,,,
,,,

,,


,,
,,
,,
,,,
,,,
,,
,,


,,
,,
,,,
,,,

,,

,,,
,,
,,


,,
,,
,,,
,,
,,
,,

,,,

,,

,,
,,
,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
Logarithmi.
,,
,,
,,

,,,

,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
,,
,,,
,,,
Num.
absolu.

,,
,,

Logarithmi.
,,

,,,
,,

127
Briggs’ 1624 table of logarithms (reconstruction, D. Roegel, 2010)
Chilias decima.
Num.
absolu.

Logarithmi.
,,,
Num.
absolu.

,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,
,,
,,,

,,,

,,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,,
,,,

,,


,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,


,,
,,
,,
,,,
,,,
,,
,,

,,,

,,
,,,

,,
,,

,,,
,,
,,
,,,

,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,
,,,
,,,

,,


,,
,,
,,
,,,
,,,
,,
,,


,,
,,
,,,
,,,

,,

,,,
,,
,,


,,
,,
,,,
,,
,,
,,

,,,

,,

,,
,,
,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
Logarithmi.
,,
,,
,,

,,,

,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
,,
,,,
,,,
Num.
absolu.

,,
,,

Logarithmi.
,,

,,,
,,

128
Briggs’ 1624 table of logarithms (reconstruction, D. Roegel, 2010)
Chilias decima.
Num.
absolu.

Logarithmi.
,,,
Num.
absolu.

,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,
,,
,,,

,,,

,,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,,
,,,

,,


,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,


,,
,,
,,
,,,
,,,
,,
,,

,,,

,,
,,,

,,
,,

,,,
,,
,,
,,,

,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,
,,,
,,,

,,


,,
,,
,,
,,,
,,,
,,
,,


,,
,,
,,,
,,,

,,

,,,
,,
,,


,,
,,
,,,
,,
,,
,,

,,,

,,

,,
,,
,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
Logarithmi.
,,
,,
,,

,,,

,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
,,
,,,
,,,
Num.
absolu.

,,
,,

Logarithmi.
,,

,,,
,,

129
Briggs’ 1624 table of logarithms (reconstruction, D. Roegel, 2010)
Chilias decima.
Num.
absolu.

Logarithmi.
,,,
Num.
absolu.

,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,
,,
,,,

,,,

,,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,,
,,,

,,


,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,


,,
,,
,,
,,,
,,,
,,
,,

,,,

,,
,,,

,,
,,

,,,
,,
,,
,,,

,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,
,,,
,,,

,,


,,
,,
,,
,,,
,,,
,,
,,


,,
,,
,,,
,,,

,,

,,,
,,
,,


,,
,,
,,,
,,
,,
,,

,,,

,,

,,
,,
,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
Logarithmi.
,,
,,
,,

,,,

,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
,,
,,,
,,,
Num.
absolu.

,,
,,

Logarithmi.
,,

,,,
,,

130
Briggs’ 1624 table of logarithms (reconstruction, D. Roegel, 2010)
Chilias decima.
Num.
absolu.

Logarithmi.
,,,
Num.
absolu.

,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,
,,
,,,

,,,

,,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,,
,,,

,,


,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,


,,
,,
,,
,,,
,,,
,,
,,

,,,

,,
,,,

,,
,,

,,,
,,
,,
,,,

,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,
,,,
,,,

,,


,,
,,
,,
,,,
,,,
,,
,,


,,
,,
,,,
,,,

,,

,,,
,,
,,


,,
,,
,,,
,,
,,
,,

,,,

,,

,,
,,
,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
Logarithmi.
,,
,,
,,

,,,

,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
,,
,,,
,,,
Num.
absolu.

,,
,,

Logarithmi.
,,

,,,
,,

131
Briggs’ 1624 table of logarithms (reconstruction, D. Roegel, 2010)
Chilias decima.
Num.
absolu.

Logarithmi.
,,,
Num.
absolu.

,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,
,,
,,,

,,,

,,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,,
,,,

,,


,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,


,,
,,
,,
,,,
,,,
,,
,,

,,,

,,
,,,

,,
,,

,,,
,,
,,
,,,

,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,
,,,
,,,

,,


,,
,,
,,
,,,
,,,
,,
,,


,,
,,
,,,
,,,

,,

,,,
,,
,,


,,
,,
,,,
,,
,,
,,

,,,

,,

,,
,,
,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
Logarithmi.
,,
,,
,,

,,,

,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
,,
,,,
,,,
Num.
absolu.

,,
,,

Logarithmi.
,,

,,,
,,

132
Briggs’ 1624 table of logarithms (reconstruction, D. Roegel, 2010)
Chilias decima.
Num.
absolu.

Logarithmi.
,,,
Num.
absolu.

,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,
,,
,,,

,,,

,,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,,
,,,

,,


,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,


,,
,,
,,
,,,
,,,
,,
,,

,,,

,,
,,,

,,
,,

,,,
,,
,,
,,,

,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,
,,,
,,,

,,


,,
,,
,,
,,,
,,,
,,
,,


,,
,,
,,,
,,,

,,

,,,
,,
,,


,,
,,
,,,
,,
,,
,,

,,,

,,

,,
,,
,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
Logarithmi.
,,
,,
,,

,,,

,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
,,
,,,
,,,
Num.
absolu.

,,
,,

Logarithmi.
,,

,,,
,,

133
Briggs’ 1624 table of logarithms (reconstruction, D. Roegel, 2010)
Chilias decima.
Num.
absolu.

Logarithmi.
,,,
Num.
absolu.

,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,
,,
,,,

,,,

,,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,,
,,,

,,


,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,


,,
,,
,,
,,,
,,,
,,
,,

,,,

,,
,,,

,,
,,

,,,
,,
,,
,,,

,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,
,,,
,,,

,,


,,
,,
,,
,,,
,,,
,,
,,


,,
,,
,,,
,,,

,,

,,,
,,
,,


,,
,,
,,,
,,
,,
,,

,,,

,,

,,
,,
,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
Logarithmi.
,,
,,
,,

,,,

,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
,,
,,,
,,,
Num.
absolu.

,,
,,

Logarithmi.
,,

,,,
,,

134
Briggs’ 1624 table of logarithms (reconstruction, D. Roegel, 2010)
Chilias vndecima.
Num.
absolu.

Logarithmi.
,,,
Num.
absolu.

,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,
,,
,,,

,,,

,,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,,
,,,

,,


,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,


,,
,,
,,
,,,
,,,
,,
,,

,,,

,,
,,,

,,
,,

,,,
,,
,,
,,,

,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,
,,,
,,,

,,


,,
,,
,,
,,,
,,,
,,
,,


,,
,,
,,,
,,,

,,

,,,
,,
,,


,,
,,
,,,
,,
,,
,,

,,,

,,

,,
,,
,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
Logarithmi.
,,
,,
,,

,,,

,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
,,
,,,
,,,
Num.
absolu.

,,
,,

Logarithmi.
,,

,,,
,,

135
Briggs’ 1624 table of logarithms (reconstruction, D. Roegel, 2010)
Chilias vndecima.
Num.
absolu.

Logarithmi.
,,,
Num.
absolu.

,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,
,,
,,,

,,,

,,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,,
,,,

,,


,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,


,,
,,
,,
,,,
,,,
,,
,,

,,,

,,
,,,

,,
,,

,,,
,,
,,
,,,

,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,
,,,
,,,

,,


,,
,,
,,
,,,
,,,
,,
,,


,,
,,
,,,
,,,

,,

,,,
,,
,,


,,
,,
,,,
,,
,,
,,

,,,

,,

,,
,,
,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
Logarithmi.
,,
,,
,,

,,,

,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
,,
,,,
,,,
Num.
absolu.

,,
,,

Logarithmi.
,,

,,,
,,

136
Briggs’ 1624 table of logarithms (reconstruction, D. Roegel, 2010)
Chilias vndecima.
Num.
absolu.

Logarithmi.
,,,
Num.
absolu.

,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,
,,
,,,

,,,

,,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,,
,,,

,,


,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,


,,
,,
,,
,,,
,,,
,,
,,

,,,

,,
,,,

,,
,,

,,,
,,
,,
,,,

,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,
,,,
,,,

,,


,,
,,
,,
,,,
,,,
,,
,,


,,
,,
,,,
,,,

,,

,,,
,,
,,


,,
,,
,,,
,,
,,
,,

,,,

,,

,,
,,
,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
Logarithmi.
,,
,,
,,

,,,

,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
,,
,,,
,,,
Num.
absolu.

,,
,,

Logarithmi.
,,

,,,
,,

137
Briggs’ 1624 table of logarithms (reconstruction, D. Roegel, 2010)
Chilias vndecima.
Num.
absolu.

Logarithmi.
,,,
Num.
absolu.

,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,
,,
,,,

,,,

,,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,,
,,,

,,


,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,


,,
,,
,,
,,,
,,,
,,
,,

,,,

,,
,,,

,,
,,

,,,
,,
,,
,,,

,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,
,,,
,,,

,,


,,
,,
,,
,,,
,,,
,,
,,


,,
,,
,,,
,,,

,,

,,,
,,
,,


,,
,,
,,,
,,
,,
,,

,,,

,,

,,
,,
,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
Logarithmi.
,,
,,
,,

,,,

,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
,,
,,,
,,,
Num.
absolu.

,,
,,

Logarithmi.
,,

,,,
,,

138
Briggs’ 1624 table of logarithms (reconstruction, D. Roegel, 2010)
Chilias vndecima.
Num.
absolu.

Logarithmi.
,,,
Num.
absolu.

,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,
,,
,,,

,,,

,,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,,
,,,

,,


,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,


,,
,,
,,
,,,
,,,
,,
,,

,,,

,,
,,,

,,
,,

,,,
,,
,,
,,,

,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,
,,,
,,,

,,


,,
,,
,,
,,,
,,,
,,
,,


,,
,,
,,,
,,,

,,

,,,
,,
,,


,,
,,
,,,
,,
,,
,,

,,,

,,

,,
,,
,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
Logarithmi.
,,
,,
,,

,,,

,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
,,
,,,
,,,
Num.
absolu.

,,
,,

Logarithmi.
,,

,,,
,,

139
Briggs’ 1624 table of logarithms (reconstruction, D. Roegel, 2010)
Chilias vndecima.
Num.
absolu.

Logarithmi.
,,,
Num.
absolu.

,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,
,,
,,,

,,,

,,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,,
,,,

,,


,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,


,,
,,
,,
,,,
,,,
,,
,,

,,,

,,
,,,

,,
,,

,,,
,,
,,
,,,

,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,
,,,
,,,

,,


,,
,,
,,
,,,
,,,
,,
,,


,,
,,
,,,
,,,

,,

,,,
,,
,,


,,
,,
,,,
,,
,,
,,

,,,

,,

,,
,,
,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
Logarithmi.
,,
,,
,,

,,,

,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
,,
,,,
,,,
Num.
absolu.

,,
,,

Logarithmi.
,,

,,,
,,

140
Briggs’ 1624 table of logarithms (reconstruction, D. Roegel, 2010)
Chilias vndecima.
Num.
absolu.

Logarithmi.
,,,
Num.
absolu.

,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,
,,
,,,

,,,

,,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,,
,,,

,,


,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,


,,
,,
,,
,,,
,,,
,,
,,

,,,

,,
,,,

,,
,,

,,,
,,
,,
,,,

,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,
,,,
,,,

,,


,,
,,
,,
,,,
,,,
,,
,,


,,
,,
,,,
,,,

,,

,,,
,,
,,


,,
,,
,,,
,,
,,
,,

,,,

,,

,,
,,
,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
Logarithmi.
,,
,,
,,

,,,

,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
,,
,,,
,,,
Num.
absolu.

,,
,,

Logarithmi.
,,

,,,
,,

141
Briggs’ 1624 table of logarithms (reconstruction, D. Roegel, 2010)
Chilias vndecima.
Num.
absolu.

Logarithmi.
,,,
Num.
absolu.

,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,
,,
,,,

,,,

,,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,,
,,,

,,


,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,


,,
,,
,,
,,,
,,,
,,
,,

,,,

,,
,,,

,,
,,

,,,
,,
,,
,,,

,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,
,,,
,,,

,,


,,
,,
,,
,,,
,,,
,,
,,


,,
,,
,,,
,,,

,,

,,,
,,
,,


,,
,,
,,,
,,
,,
,,

,,,

,,

,,
,,
,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
Logarithmi.
,,
,,
,,

,,,

,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
,,
,,,
,,,
Num.
absolu.

,,
,,

Logarithmi.
,,

,,,
,,

142
Briggs’ 1624 table of logarithms (reconstruction, D. Roegel, 2010)
Chilias vndecima.
Num.
absolu.

Logarithmi.
,,,
Num.
absolu.

,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,
,,
,,,

,,,

,,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,,
,,,

,,


,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,


,,
,,
,,
,,,
,,,
,,
,,

,,,

,,
,,,

,,
,,

,,,
,,
,,
,,,

,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,
,,,
,,,

,,


,,
,,
,,
,,,
,,,
,,
,,


,,
,,
,,,
,,,

,,

,,,
,,
,,


,,
,,
,,,
,,
,,
,,

,,,

,,

,,
,,
,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
Logarithmi.
,,
,,
,,

,,,

,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
,,
,,,
,,,
Num.
absolu.

,,
,,

Logarithmi.
,,

,,,
,,

143
Briggs’ 1624 table of logarithms (reconstruction, D. Roegel, 2010)
Chilias vndecima.
Num.
absolu.

Logarithmi.
,,,
Num.
absolu.

,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,
,,
,,,

,,,

,,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,,
,,,

,,


,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,


,,
,,
,,
,,,
,,,
,,
,,

,,,

,,
,,,

,,
,,

,,,
,,
,,
,,,

,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,
,,,
,,,

,,


,,
,,
,,
,,,
,,,
,,
,,


,,
,,
,,,
,,,

,,

,,,
,,
,,


,,
,,
,,,
,,
,,
,,

,,,

,,

,,
,,
,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
Logarithmi.
,,
,,
,,

,,,

,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
,,
,,,
,,,
Num.
absolu.

,,
,,

Logarithmi.
,,

,,,
,,

144
Briggs’ 1624 table of logarithms (reconstruction, D. Roegel, 2010)
Chilias duodecima.
Num.
absolu.

Logarithmi.
,,,
Num.
absolu.

,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,
,,
,,,

,,,

,,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,,
,,,

,,


,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,


,,
,,
,,
,,,
,,,
,,
,,

,,,

,,
,,,

,,
,,

,,,
,,
,,
,,,

,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,
,,,
,,,

,,


,,
,,
,,
,,,
,,,
,,
,,


,,
,,
,,,
,,,

,,

,,,
,,
,,


,,
,,
,,,
,,
,,
,,

,,,

,,

,,
,,
,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
Logarithmi.
,,
,,
,,

,,,

,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
,,
,,,
,,,
Num.
absolu.

,,
,,

Logarithmi.
,,

,,,
,,

145
Briggs’ 1624 table of logarithms (reconstruction, D. Roegel, 2010)
Chilias duodecima.
Num.
absolu.

Logarithmi.
,,,
Num.
absolu.

,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,
,,
,,,

,,,

,,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,,
,,,

,,


,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,


,,
,,
,,
,,,
,,,
,,
,,

,,,

,,
,,,

,,
,,

,,,
,,
,,
,,,

,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,
,,,
,,,

,,


,,
,,
,,
,,,
,,,
,,
,,


,,
,,
,,,
,,,

,,

,,,
,,
,,


,,
,,
,,,
,,
,,
,,

,,,

,,

,,
,,
,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
Logarithmi.
,,
,,
,,

,,,

,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
,,
,,,
,,,
Num.
absolu.

,,
,,

Logarithmi.
,,

,,,
,,

146
Briggs’ 1624 table of logarithms (reconstruction, D. Roegel, 2010)
Chilias duodecima.
Num.
absolu.

Logarithmi.
,,,
Num.
absolu.

,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,
,,
,,,

,,,

,,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,,
,,,

,,


,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,


,,
,,
,,
,,,
,,,
,,
,,

,,,

,,
,,,

,,
,,

,,,
,,
,,
,,,

,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,
,,,
,,,

,,


,,
,,
,,
,,,
,,,
,,
,,


,,
,,
,,,
,,,

,,

,,,
,,
,,


,,
,,
,,,
,,
,,
,,

,,,

,,

,,
,,
,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
Logarithmi.
,,
,,
,,

,,,

,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
,,
,,,
,,,
Num.
absolu.

,,
,,

Logarithmi.
,,

,,,
,,

147
Briggs’ 1624 table of logarithms (reconstruction, D. Roegel, 2010)
Chilias duodecima.
Num.
absolu.

Logarithmi.
,,,
Num.
absolu.

,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,
,,
,,,

,,,

,,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,,
,,,

,,


,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,


,,
,,
,,
,,,
,,,
,,
,,

,,,

,,
,,,

,,
,,

,,,
,,
,,
,,,

,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,
,,,
,,,

,,


,,
,,
,,
,,,
,,,
,,
,,


,,
,,
,,,
,,,

,,

,,,
,,
,,


,,
,,
,,,
,,
,,
,,

,,,

,,

,,
,,
,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
Logarithmi.
,,
,,
,,

,,,

,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
,,
,,,
,,,
Num.
absolu.

,,
,,

Logarithmi.
,,

,,,
,,

148
Briggs’ 1624 table of logarithms (reconstruction, D. Roegel, 2010)
Chilias duodecima.
Num.
absolu.

Logarithmi.
,,,
Num.
absolu.

,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,
,,
,,,

,,,

,,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,,
,,,

,,


,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,


,,
,,
,,
,,,
,,,
,,
,,

,,,

,,
,,,

,,
,,

,,,
,,
,,
,,,

,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,
,,,
,,,

,,


,,
,,
,,
,,,
,,,
,,
,,


,,
,,
,,,
,,,

,,

,,,
,,
,,


,,
,,
,,,
,,
,,
,,

,,,

,,

,,
,,
,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
Logarithmi.
,,
,,
,,

,,,

,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
,,
,,,
,,,
Num.
absolu.

,,
,,

Logarithmi.
,,

,,,
,,

149
Briggs’ 1624 table of logarithms (reconstruction, D. Roegel, 2010)
Chilias duodecima.
Num.
absolu.

Logarithmi.
,,,
Num.
absolu.

,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,
,,
,,,

,,,

,,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,,
,,,

,,


,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,


,,
,,
,,
,,,
,,,
,,
,,

,,,

,,
,,,

,,
,,

,,,
,,
,,
,,,

,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,
,,,
,,,

,,


,,
,,
,,
,,,
,,,
,,
,,


,,
,,
,,,
,,,

,,

,,,
,,
,,


,,
,,
,,,
,,
,,
,,

,,,

,,

,,
,,
,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
Logarithmi.
,,
,,
,,

,,,

,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
,,
,,,
,,,
Num.
absolu.

,,
,,

Logarithmi.
,,

,,,
,,

150
Briggs’ 1624 table of logarithms (reconstruction, D. Roegel, 2010)
Chilias duodecima.
Num.
absolu.

Logarithmi.
,,,
Num.
absolu.

,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,
,,
,,,

,,,

,,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,,
,,,

,,


,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,


,,
,,
,,
,,,
,,,
,,
,,

,,,

,,
,,,

,,
,,

,,,
,,
,,
,,,

,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,
,,,
,,,

,,


,,
,,
,,
,,,
,,,
,,
,,


,,
,,
,,,
,,,

,,

,,,
,,
,,


,,
,,
,,,
,,
,,
,,

,,,

,,

,,
,,
,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
Logarithmi.
,,
,,
,,

,,,

,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
,,
,,,
,,,
Num.
absolu.

,,
,,

Logarithmi.
,,

,,,
,,

151
Briggs’ 1624 table of logarithms (reconstruction, D. Roegel, 2010)
Chilias duodecima.
Num.
absolu.

Logarithmi.
,,,
Num.
absolu.

,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,
,,
,,,

,,,

,,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,,
,,,

,,


,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,


,,
,,
,,
,,,
,,,
,,
,,

,,,

,,
,,,

,,
,,

,,,
,,
,,
,,,

,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,
,,,
,,,

,,


,,
,,
,,
,,,
,,,
,,
,,


,,
,,
,,,
,,,

,,

,,,
,,
,,


,,
,,
,,,
,,
,,
,,

,,,

,,

,,
,,
,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
Logarithmi.
,,
,,
,,

,,,

,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
,,
,,,
,,,
Num.
absolu.

,,
,,

Logarithmi.
,,

,,,
,,

152
Briggs’ 1624 table of logarithms (reconstruction, D. Roegel, 2010)
Chilias duodecima.
Num.
absolu.

Logarithmi.
,,,
Num.
absolu.

,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,
,,
,,,

,,,

,,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,,
,,,

,,


,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,


,,
,,
,,
,,,
,,,
,,
,,

,,,

,,
,,,

,,
,,

,,,
,,
,,
,,,

,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,
,,,
,,,

,,


,,
,,
,,
,,,
,,,
,,
,,


,,
,,
,,,
,,,

,,

,,,
,,
,,


,,
,,
,,,
,,
,,
,,

,,,

,,

,,
,,
,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
Logarithmi.
,,
,,
,,

,,,

,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
,,
,,,
,,,
Num.
absolu.

,,
,,

Logarithmi.
,,

,,,
,,

153
Briggs’ 1624 table of logarithms (reconstruction, D. Roegel, 2010)
Chilias duodecima.
Num.
absolu.

Logarithmi.
,,,
Num.
absolu.

,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,
,,
,,,

,,,

,,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,,
,,,

,,


,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,


,,
,,
,,
,,,
,,,
,,
,,

,,,

,,
,,,

,,
,,

,,,
,,
,,
,,,

,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,
,,,
,,,

,,


,,
,,
,,
,,,
,,,
,,
,,


,,
,,
,,,
,,,

,,

,,,
,,
,,


,,
,,
,,,
,,
,,
,,

,,,

,,

,,
,,
,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
Logarithmi.
,,
,,
,,

,,,

,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
,,
,,,
,,,
Num.
absolu.

,,
,,

Logarithmi.
,,

,,,
,,

154
Briggs’ 1624 table of logarithms (reconstruction, D. Roegel, 2010)
Chilias decimatertia.
Num.
absolu.

Logarithmi.
,,,
Num.
absolu.

,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,
,,
,,,

,,,

,,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,,
,,,

,,


,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,


,,
,,
,,
,,,
,,,
,,
,,

,,,

,,
,,,

,,
,,

,,,
,,
,,
,,,

,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,
,,,
,,,

,,


,,
,,
,,
,,,
,,,
,,
,,


,,
,,
,,,
,,,

,,

,,,
,,
,,


,,
,,
,,,
,,
,,
,,

,,,

,,

,,
,,
,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
Logarithmi.
,,
,,
,,

,,,

,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
,,
,,,
,,,
Num.
absolu.

,,
,,

Logarithmi.
,,

,,,
,,

155
Briggs’ 1624 table of logarithms (reconstruction, D. Roegel, 2010)
Chilias decimatertia.
Num.
absolu.

Logarithmi.
,,,
Num.
absolu.

,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,
,,
,,,

,,,

,,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,,
,,,

,,


,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,


,,
,,
,,
,,,
,,,
,,
,,

,,,

,,
,,,

,,
,,

,,,
,,
,,
,,,

,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,
,,,
,,,

,,


,,
,,
,,
,,,
,,,
,,
,,


,,
,,
,,,
,,,

,,

,,,
,,
,,


,,
,,
,,,
,,
,,
,,

,,,

,,

,,
,,
,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
Logarithmi.
,,
,,
,,

,,,

,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
,,
,,,
,,,
Num.
absolu.

,,
,,

Logarithmi.
,,

,,,
,,

156
Briggs’ 1624 table of logarithms (reconstruction, D. Roegel, 2010)
Chilias decimatertia.
Num.
absolu.

Logarithmi.
,,,
Num.
absolu.

,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,
,,
,,,

,,,

,,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,,
,,,

,,


,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,


,,
,,
,,
,,,
,,,
,,
,,

,,,

,,
,,,

,,
,,

,,,
,,
,,
,,,

,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,
,,,
,,,

,,


,,
,,
,,
,,,
,,,
,,
,,


,,
,,
,,,
,,,

,,

,,,
,,
,,


,,
,,
,,,
,,
,,
,,

,,,

,,

,,
,,
,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
Logarithmi.
,,
,,
,,

,,,

,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
,,
,,,
,,,
Num.
absolu.

,,
,,

Logarithmi.
,,

,,,
,,

157
Briggs’ 1624 table of logarithms (reconstruction, D. Roegel, 2010)
Chilias decimatertia.
Num.
absolu.

Logarithmi.
,,,
Num.
absolu.

,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,
,,
,,,

,,,

,,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,,
,,,

,,


,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,


,,
,,
,,
,,,
,,,
,,
,,

,,,

,,
,,,

,,
,,

,,,
,,
,,
,,,

,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,
,,,
,,,

,,


,,
,,
,,
,,,
,,,
,,
,,


,,
,,
,,,
,,,

,,

,,,
,,
,,


,,
,,
,,,
,,
,,
,,

,,,

,,

,,
,,
,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
Logarithmi.
,,
,,
,,

,,,

,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
,,
,,,
,,,
Num.
absolu.

,,
,,

Logarithmi.
,,

,,,
,,

158
Briggs’ 1624 table of logarithms (reconstruction, D. Roegel, 2010)
Chilias decimatertia.
Num.
absolu.

Logarithmi.
,,,
Num.
absolu.

,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,
,,
,,,

,,,

,,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,,
,,,

,,


,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,


,,
,,
,,
,,,
,,,
,,
,,

,,,

,,
,,,

,,
,,

,,,
,,
,,
,,,

,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,
,,,
,,,

,,


,,
,,
,,
,,,
,,,
,,
,,


,,
,,
,,,
,,,

,,

,,,
,,
,,


,,
,,
,,,
,,
,,
,,

,,,

,,

,,
,,
,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
Logarithmi.
,,
,,
,,

,,,

,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
,,
,,,
,,,
Num.
absolu.

,,
,,

Logarithmi.
,,

,,,
,,

159
Briggs’ 1624 table of logarithms (reconstruction, D. Roegel, 2010)
Chilias decimatertia.
Num.
absolu.

Logarithmi.
,,,
Num.
absolu.

,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,
,,
,,,

,,,

,,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,,
,,,

,,


,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,


,,
,,
,,
,,,
,,,
,,
,,

,,,

,,
,,,

,,
,,

,,,
,,
,,
,,,

,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,
,,,
,,,

,,


,,
,,
,,
,,,
,,,
,,
,,


,,
,,
,,,
,,,

,,

,,,
,,
,,


,,
,,
,,,
,,
,,
,,

,,,

,,

,,
,,
,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
Logarithmi.
,,
,,
,,

,,,

,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
,,
,,,
,,,
Num.
absolu.

,,
,,

Logarithmi.
,,

,,,
,,

160
Briggs’ 1624 table of logarithms (reconstruction, D. Roegel, 2010)
Chilias decimatertia.
Num.
absolu.

Logarithmi.
,,,
Num.
absolu.

,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,
,,
,,,

,,,

,,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,,
,,,

,,


,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,


,,
,,
,,
,,,
,,,
,,
,,

,,,

,,
,,,

,,
,,

,,,
,,
,,
,,,

,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,
,,,
,,,

,,


,,
,,
,,
,,,
,,,
,,
,,


,,
,,
,,,
,,,

,,

,,,
,,
,,


,,
,,
,,,
,,
,,
,,

,,,

,,

,,
,,
,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
Logarithmi.
,,
,,
,,

,,,

,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
,,
,,,
,,,
Num.
absolu.

,,
,,

Logarithmi.
,,

,,,
,,

161
Briggs’ 1624 table of logarithms (reconstruction, D. Roegel, 2010)
Chilias decimatertia.
Num.
absolu.

Logarithmi.
,,,
Num.
absolu.

,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,
,,
,,,

,,,

,,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,,
,,,

,,


,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,


,,
,,
,,
,,,
,,,
,,
,,

,,,

,,
,,,

,,
,,

,,,
,,
,,
,,,

,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,
,,,
,,,

,,


,,
,,
,,
,,,
,,,
,,
,,


,,
,,
,,,
,,,

,,

,,,
,,
,,


,,
,,
,,,
,,
,,
,,

,,,

,,

,,
,,
,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
Logarithmi.
,,
,,
,,

,,,

,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
,,
,,,
,,,
Num.
absolu.

,,
,,

Logarithmi.
,,

,,,
,,

162
Briggs’ 1624 table of logarithms (reconstruction, D. Roegel, 2010)
Chilias decimatertia.
Num.
absolu.

Logarithmi.
,,,
Num.
absolu.

,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,
,,
,,,

,,,

,,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,,
,,,

,,


,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,


,,
,,
,,
,,,
,,,
,,
,,

,,,

,,
,,,

,,
,,

,,,
,,
,,
,,,

,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,
,,,
,,,

,,


,,
,,
,,
,,,
,,,
,,
,,


,,
,,
,,,
,,,

,,

,,,
,,
,,


,,
,,
,,,
,,
,,
,,

,,,

,,

,,
,,
,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
Logarithmi.
,,
,,
,,

,,,

,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
,,
,,,
,,,
Num.
absolu.

,,
,,

Logarithmi.
,,

,,,
,,

163
Briggs’ 1624 table of logarithms (reconstruction, D. Roegel, 2010)
Chilias decimatertia.
Num.
absolu.

Logarithmi.
,,,
Num.
absolu.

,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,
,,
,,,

,,,

,,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,,
,,,

,,


,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,


,,
,,
,,
,,,
,,,
,,
,,

,,,

,,
,,,

,,
,,

,,,
,,
,,
,,,

,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,
,,,
,,,

,,


,,
,,
,,
,,,
,,,
,,
,,


,,
,,
,,,
,,,

,,

,,,
,,
,,


,,
,,
,,,
,,
,,
,,

,,,

,,

,,
,,
,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
Logarithmi.
,,
,,
,,

,,,

,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
,,
,,,
,,,
Num.
absolu.

,,
,,

Logarithmi.
,,

,,,
,,

164
Briggs’ 1624 table of logarithms (reconstruction, D. Roegel, 2010)
Chilias decimaquarta.
Num.
absolu.

Logarithmi.
,,,
Num.
absolu.

,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,
,,
,,,

,,,

,,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,,
,,,

,,


,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,


,,
,,
,,
,,,
,,,
,,
,,

,,,

,,
,,,

,,
,,

,,,
,,
,,
,,,

,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,
,,,
,,,

,,


,,
,,
,,
,,,
,,,
,,
,,


,,
,,
,,,
,,,

,,

,,,
,,
,,


,,
,,
,,,
,,
,,
,,

,,,

,,

,,
,,
,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
Logarithmi.
,,
,,
,,

,,,

,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
,,
,,,
,,,
Num.
absolu.

,,
,,

Logarithmi.
,,

,,,
,,

165
Briggs’ 1624 table of logarithms (reconstruction, D. Roegel, 2010)
Chilias decimaquarta.
Num.
absolu.

Logarithmi.
,,,
Num.
absolu.

,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,
,,
,,,

,,,

,,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,,
,,,

,,


,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,


,,
,,
,,
,,,
,,,
,,
,,

,,,

,,
,,,

,,
,,

,,,
,,
,,
,,,

,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,
,,,
,,,

,,


,,
,,
,,
,,,
,,,
,,
,,


,,
,,
,,,
,,,

,,

,,,
,,
,,


,,
,,
,,,
,,
,,
,,

,,,

,,

,,
,,
,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
Logarithmi.
,,
,,
,,

,,,

,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
,,
,,,
,,,
Num.
absolu.

,,
,,

Logarithmi.
,,

,,,
,,

166
Briggs’ 1624 table of logarithms (reconstruction, D. Roegel, 2010)
Chilias decimaquarta.
Num.
absolu.

Logarithmi.
,,,
Num.
absolu.

,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,
,,
,,,

,,,

,,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,,
,,,

,,


,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,


,,
,,
,,
,,,
,,,
,,
,,

,,,

,,
,,,

,,
,,

,,,
,,
,,
,,,

,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,
,,,
,,,

,,


,,
,,
,,
,,,
,,,
,,
,,


,,
,,
,,,
,,,

,,

,,,
,,
,,


,,
,,
,,,
,,
,,
,,

,,,

,,

,,
,,
,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
Logarithmi.
,,
,,
,,

,,,

,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
,,
,,,
,,,
Num.
absolu.

,,
,,

Logarithmi.
,,

,,,
,,

167
Briggs’ 1624 table of logarithms (reconstruction, D. Roegel, 2010)
Chilias decimaquarta.
Num.
absolu.

Logarithmi.
,,,
Num.
absolu.

,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,
,,
,,,

,,,

,,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,,
,,,

,,


,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,


,,
,,
,,
,,,
,,,
,,
,,

,,,

,,
,,,

,,
,,

,,,
,,
,,
,,,

,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,
,,,
,,,

,,


,,
,,
,,
,,,
,,,
,,
,,


,,
,,
,,,
,,,

,,

,,,
,,
,,


,,
,,
,,,
,,
,,
,,

,,,

,,

,,
,,
,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
Logarithmi.
,,
,,
,,

,,,

,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
,,
,,,
,,,
Num.
absolu.

,,
,,

Logarithmi.
,,

,,,
,,

168
Briggs’ 1624 table of logarithms (reconstruction, D. Roegel, 2010)
Chilias decimaquarta.
Num.
absolu.

Logarithmi.
,,,
Num.
absolu.

,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,
,,
,,,

,,,

,,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,,
,,,

,,


,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,


,,
,,
,,
,,,
,,,
,,
,,

,,,

,,
,,,

,,
,,

,,,
,,
,,
,,,

,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,
,,,
,,,

,,


,,
,,
,,
,,,
,,,
,,
,,


,,
,,
,,,
,,,

,,

,,,
,,
,,


,,
,,
,,,
,,
,,
,,

,,,

,,

,,
,,
,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
Logarithmi.
,,
,,
,,

,,,

,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
,,
,,,
,,,
Num.
absolu.

,,
,,

Logarithmi.
,,

,,,
,,

169
Briggs’ 1624 table of logarithms (reconstruction, D. Roegel, 2010)
Chilias decimaquarta.
Num.
absolu.

Logarithmi.
,,,
Num.
absolu.

,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,
,,
,,,

,,,

,,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,,
,,,

,,


,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,


,,
,,
,,
,,,
,,,
,,
,,

,,,

,,
,,,

,,
,,

,,,
,,
,,
,,,

,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,
,,,
,,,

,,


,,
,,
,,
,,,
,,,
,,
,,


,,
,,
,,,
,,,

,,

,,,
,,
,,


,,
,,
,,,
,,
,,
,,

,,,

,,

,,
,,
,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
Logarithmi.
,,
,,
,,

,,,

,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
,,
,,,
,,,
Num.
absolu.

,,
,,

Logarithmi.
,,

,,,
,,

170
Briggs’ 1624 table of logarithms (reconstruction, D. Roegel, 2010)
Chilias decimaquarta.
Num.
absolu.

Logarithmi.
,,,
Num.
absolu.

,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,
,,
,,,

,,,

,,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,,
,,,

,,


,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,


,,
,,
,,
,,,
,,,
,,
,,

,,,

,,
,,,

,,
,,

,,,
,,
,,
,,,

,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,
,,,
,,,

,,


,,
,,
,,
,,,
,,,
,,
,,


,,
,,
,,,
,,,

,,

,,,
,,
,,


,,
,,
,,,
,,
,,
,,

,,,

,,

,,
,,
,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
Logarithmi.
,,
,,
,,

,,,

,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
,,
,,,
,,,
Num.
absolu.

,,
,,

Logarithmi.
,,

,,,
,,

171
Briggs’ 1624 table of logarithms (reconstruction, D. Roegel, 2010)
Chilias decimaquarta.
Num.
absolu.

Logarithmi.
,,,
Num.
absolu.

,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,
,,
,,,

,,,

,,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,,
,,,

,,


,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,


,,
,,
,,
,,,
,,,
,,
,,

,,,

,,
,,,

,,
,,

,,,
,,
,,
,,,

,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,
,,,
,,,

,,


,,
,,
,,
,,,
,,,
,,
,,


,,
,,
,,,
,,,

,,

,,,
,,
,,


,,
,,
,,,
,,
,,
,,

,,,

,,

,,
,,
,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
Logarithmi.
,,
,,
,,

,,,

,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
,,
,,,
,,,
Num.
absolu.

,,
,,

Logarithmi.
,,

,,,
,,

172
Briggs’ 1624 table of logarithms (reconstruction, D. Roegel, 2010)
Chilias decimaquarta.
Num.
absolu.

Logarithmi.
,,,
Num.
absolu.

,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,
,,
,,,

,,,

,,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,,
,,,

,,


,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,


,,
,,
,,
,,,
,,,
,,
,,

,,,

,,
,,,

,,
,,

,,,
,,
,,
,,,

,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,
,,,
,,,

,,


,,
,,
,,
,,,
,,,
,,
,,


,,
,,
,,,
,,,

,,

,,,
,,
,,


,,
,,
,,,
,,
,,
,,

,,,

,,

,,
,,
,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
Logarithmi.
,,
,,
,,

,,,

,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
,,
,,,
,,,
Num.
absolu.

,,
,,

Logarithmi.
,,

,,,
,,

173
Briggs’ 1624 table of logarithms (reconstruction, D. Roegel, 2010)
Chilias decimaquarta.
Num.
absolu.

Logarithmi.
,,,
Num.
absolu.

,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,
,,
,,,

,,,

,,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,,
,,,

,,


,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,


,,
,,
,,
,,,
,,,
,,
,,

,,,

,,
,,,

,,
,,

,,,
,,
,,
,,,

,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,
,,,
,,,

,,


,,
,,
,,
,,,
,,,
,,
,,


,,
,,
,,,
,,,

,,

,,,
,,
,,


,,
,,
,,,
,,
,,
,,

,,,

,,

,,
,,
,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
Logarithmi.
,,
,,
,,

,,,

,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
,,
,,,
,,,
Num.
absolu.

,,
,,

Logarithmi.
,,

,,,
,,

174
Briggs’ 1624 table of logarithms (reconstruction, D. Roegel, 2010)
Chilias decimaquinta.
Num.
absolu.

Logarithmi.
,,,
Num.
absolu.

,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,
,,
,,,

,,,

,,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,,
,,,

,,


,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,


,,
,,
,,
,,,
,,,
,,
,,

,,,

,,
,,,

,,
,,

,,,
,,
,,
,,,

,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,
,,,
,,,

,,


,,
,,
,,
,,,
,,,
,,
,,


,,
,,
,,,
,,,

,,

,,,
,,
,,


,,
,,
,,,
,,
,,
,,

,,,

,,

,,
,,
,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
Logarithmi.
,,
,,
,,

,,,

,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
,,
,,,
,,,
Num.
absolu.

,,
,,

Logarithmi.
,,

,,,
,,

175
Briggs’ 1624 table of logarithms (reconstruction, D. Roegel, 2010)
Chilias decimaquinta.
Num.
absolu.

Logarithmi.
,,,
Num.
absolu.

,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,
,,
,,,

,,,

,,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,,
,,,

,,


,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,


,,
,,
,,
,,,
,,,
,,
,,

,,,

,,
,,,

,,
,,

,,,
,,
,,
,,,

,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,
,,,
,,,

,,


,,
,,
,,
,,,
,,,
,,
,,


,,
,,
,,,
,,,

,,

,,,
,,
,,


,,
,,
,,,
,,
,,
,,

,,,

,,

,,
,,
,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
Logarithmi.
,,
,,
,,

,,,

,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
,,
,,,
,,,
Num.
absolu.

,,
,,

Logarithmi.
,,

,,,
,,

176
Briggs’ 1624 table of logarithms (reconstruction, D. Roegel, 2010)
Chilias decimaquinta.
Num.
absolu.

Logarithmi.
,,,
Num.
absolu.

,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,
,,
,,,

,,,

,,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,,
,,,

,,


,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,


,,
,,
,,
,,,
,,,
,,
,,

,,,

,,
,,,

,,
,,

,,,
,,
,,
,,,

,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,
,,,
,,,

,,


,,
,,
,,
,,,
,,,
,,
,,


,,
,,
,,,
,,,

,,

,,,
,,
,,


,,
,,
,,,
,,
,,
,,

,,,

,,

,,
,,
,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
Logarithmi.
,,
,,
,,

,,,

,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
,,
,,,
,,,
Num.
absolu.

,,
,,

Logarithmi.
,,

,,,
,,

177
Briggs’ 1624 table of logarithms (reconstruction, D. Roegel, 2010)
Chilias decimaquinta.
Num.
absolu.

Logarithmi.
,,,
Num.
absolu.

,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,
,,
,,,

,,,

,,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,,
,,,

,,


,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,


,,
,,
,,
,,,
,,,
,,
,,

,,,

,,
,,,

,,
,,

,,,
,,
,,
,,,

,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,
,,,
,,,

,,


,,
,,
,,
,,,
,,,
,,
,,


,,
,,
,,,
,,,

,,

,,,
,,
,,


,,
,,
,,,
,,
,,
,,

,,,

,,

,,
,,
,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
Logarithmi.
,,
,,
,,

,,,

,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
,,
,,,
,,,
Num.
absolu.

,,
,,

Logarithmi.
,,

,,,
,,

178
Briggs’ 1624 table of logarithms (reconstruction, D. Roegel, 2010)
Chilias decimaquinta.
Num.
absolu.

Logarithmi.
,,,
Num.
absolu.

,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,
,,
,,,

,,,

,,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,,
,,,

,,


,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,


,,
,,
,,
,,,
,,,
,,
,,

,,,

,,
,,,

,,
,,

,,,
,,
,,
,,,

,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,
,,,
,,,

,,


,,
,,
,,
,,,
,,,
,,
,,


,,
,,
,,,
,,,

,,

,,,
,,
,,


,,
,,
,,,
,,
,,
,,

,,,

,,

,,
,,
,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
Logarithmi.
,,
,,
,,

,,,

,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
,,
,,,
,,,
Num.
absolu.

,,
,,

Logarithmi.
,,

,,,
,,

179
Briggs’ 1624 table of logarithms (reconstruction, D. Roegel, 2010)
Chilias decimaquinta.
Num.
absolu.

Logarithmi.
,,,
Num.
absolu.

,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,
,,
,,,

,,,

,,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,,
,,,

,,


,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,


,,
,,
,,
,,,
,,,
,,
,,

,,,

,,
,,,

,,
,,

,,,
,,
,,
,,,

,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,
,,,
,,,

,,


,,
,,
,,
,,,
,,,
,,
,,


,,
,,
,,,
,,,

,,

,,,
,,
,,


,,
,,
,,,
,,
,,
,,

,,,

,,

,,
,,
,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
Logarithmi.
,,
,,
,,

,,,

,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
,,
,,,
,,,
Num.
absolu.

,,
,,

Logarithmi.
,,

,,,
,,

180
Briggs’ 1624 table of logarithms (reconstruction, D. Roegel, 2010)
Chilias decimaquinta.
Num.
absolu.

Logarithmi.
,,,
Num.
absolu.

,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,
,,
,,,

,,,

,,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,,
,,,

,,


,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,


,,
,,
,,
,,,
,,,
,,
,,

,,,

,,
,,,

,,
,,

,,,
,,
,,
,,,

,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,
,,,
,,,

,,


,,
,,
,,
,,,
,,,
,,
,,


,,
,,
,,,
,,,

,,

,,,
,,
,,


,,
,,
,,,
,,
,,
,,

,,,

,,

,,
,,
,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
Logarithmi.
,,
,,
,,

,,,

,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
,,
,,,
,,,
Num.
absolu.

,,
,,

Logarithmi.
,,

,,,
,,

181
Briggs’ 1624 table of logarithms (reconstruction, D. Roegel, 2010)
Chilias decimaquinta.
Num.
absolu.

Logarithmi.
,,,
Num.
absolu.

,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,
,,
,,,

,,,

,,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,,
,,,

,,


,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,


,,
,,
,,
,,,
,,,
,,
,,

,,,

,,
,,,

,,
,,

,,,
,,
,,
,,,

,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,
,,,
,,,

,,


,,
,,
,,
,,,
,,,
,,
,,


,,
,,
,,,
,,,

,,

,,,
,,
,,


,,
,,
,,,
,,
,,
,,

,,,

,,

,,
,,
,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
Logarithmi.
,,
,,
,,

,,,

,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
,,
,,,
,,,
Num.
absolu.

,,
,,

Logarithmi.
,,

,,,
,,

182
Briggs’ 1624 table of logarithms (reconstruction, D. Roegel, 2010)
Chilias decimaquinta.
Num.
absolu.

Logarithmi.
,,,
Num.
absolu.

,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,
,,
,,,

,,,

,,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,,
,,,

,,


,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,


,,
,,
,,
,,,
,,,
,,
,,

,,,

,,
,,,

,,
,,

,,,
,,
,,
,,,

,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,
,,,
,,,

,,


,,
,,
,,
,,,
,,,
,,
,,


,,
,,
,,,
,,,

,,

,,,
,,
,,


,,
,,
,,,
,,
,,
,,

,,,

,,

,,
,,
,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
Logarithmi.
,,
,,
,,

,,,

,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
,,
,,,
,,,
Num.
absolu.

,,
,,

Logarithmi.
,,

,,,
,,

183
Briggs’ 1624 table of logarithms (reconstruction, D. Roegel, 2010)
Chilias decimaquinta.
Num.
absolu.

Logarithmi.
,,,
Num.
absolu.

,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,
,,
,,,

,,,

,,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,,
,,,

,,


,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,


,,
,,
,,
,,,
,,,
,,
,,

,,,

,,
,,,

,,
,,

,,,
,,
,,
,,,

,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,
,,,
,,,

,,


,,
,,
,,
,,,
,,,
,,
,,


,,
,,
,,,
,,,

,,

,,,
,,
,,


,,
,,
,,,
,,
,,
,,

,,,

,,

,,
,,
,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
Logarithmi.
,,
,,
,,

,,,

,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
,,
,,,
,,,
Num.
absolu.

,,
,,

Logarithmi.
,,

,,,
,,

184
Briggs’ 1624 table of logarithms (reconstruction, D. Roegel, 2010)
Chilias decimasexta.
Num.
absolu.

Logarithmi.
,,,
Num.
absolu.

,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,
,,
,,,

,,,

,,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,,
,,,

,,


,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,


,,
,,
,,
,,,
,,,
,,
,,

,,,

,,
,,,

,,
,,

,,,
,,
,,
,,,

,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,
,,,
,,,

,,


,,
,,
,,
,,,
,,,
,,
,,


,,
,,
,,,
,,,

,,

,,,
,,
,,


,,
,,
,,,
,,
,,
,,

,,,

,,

,,
,,
,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
Logarithmi.
,,
,,
,,

,,,

,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
,,
,,,
,,,
Num.
absolu.

,,
,,

Logarithmi.
,,

,,,
,,

185
Briggs’ 1624 table of logarithms (reconstruction, D. Roegel, 2010)
Chilias decimasexta.
Num.
absolu.

Logarithmi.
,,,
Num.
absolu.

,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,
,,
,,,

,,,

,,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,,
,,,

,,


,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,


,,
,,
,,
,,,
,,,
,,
,,

,,,

,,
,,,

,,
,,

,,,
,,
,,
,,,

,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,
,,,
,,,

,,


,,
,,
,,
,,,
,,,
,,
,,


,,
,,
,,,
,,,

,,

,,,
,,
,,


,,
,,
,,,
,,
,,
,,

,,,

,,

,,
,,
,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
Logarithmi.
,,
,,
,,

,,,

,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
,,
,,,
,,,
Num.
absolu.

,,
,,

Logarithmi.
,,

,,,
,,

186
Briggs’ 1624 table of logarithms (reconstruction, D. Roegel, 2010)
Chilias decimasexta.
Num.
absolu.

Logarithmi.
,,,
Num.
absolu.

,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,
,,
,,,

,,,

,,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,,
,,,

,,


,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,


,,
,,
,,
,,,
,,,
,,
,,

,,,

,,
,,,

,,
,,

,,,
,,
,,
,,,

,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,
,,,
,,,

,,


,,
,,
,,
,,,
,,,
,,
,,


,,
,,
,,,
,,,

,,

,,,
,,
,,


,,
,,
,,,
,,
,,
,,

,,,

,,

,,
,,
,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
Logarithmi.
,,
,,
,,

,,,

,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
,,
,,,
,,,
Num.
absolu.

,,
,,

Logarithmi.
,,

,,,
,,

187
Briggs’ 1624 table of logarithms (reconstruction, D. Roegel, 2010)
Chilias decimasexta.
Num.
absolu.

Logarithmi.
,,,
Num.
absolu.

,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,
,,
,,,

,,,

,,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,,
,,,

,,


,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,


,,
,,
,,
,,,
,,,
,,
,,

,,,

,,
,,,

,,
,,

,,,
,,
,,
,,,

,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,
,,,
,,,

,,


,,
,,
,,
,,,
,,,
,,
,,


,,
,,
,,,
,,,

,,

,,,
,,
,,


,,
,,
,,,
,,
,,
,,

,,,

,,

,,
,,
,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
Logarithmi.
,,
,,
,,

,,,

,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
,,
,,,
,,,
Num.
absolu.

,,
,,

Logarithmi.
,,

,,,
,,

188
Briggs’ 1624 table of logarithms (reconstruction, D. Roegel, 2010)
Chilias decimasexta.
Num.
absolu.

Logarithmi.
,,,
Num.
absolu.

,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,
,,
,,,

,,,

,,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,,
,,,

,,


,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,


,,
,,
,,
,,,
,,,
,,
,,

,,,

,,
,,,

,,
,,

,,,
,,
,,
,,,

,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,
,,,
,,,

,,


,,
,,
,,
,,,
,,,
,,
,,


,,
,,
,,,
,,,

,,

,,,
,,
,,


,,
,,
,,,
,,
,,
,,

,,,

,,

,,
,,
,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
Logarithmi.
,,
,,
,,

,,,

,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
,,
,,,
,,,
Num.
absolu.

,,
,,

Logarithmi.
,,

,,,
,,

189
Briggs’ 1624 table of logarithms (reconstruction, D. Roegel, 2010)
Chilias decimasexta.
Num.
absolu.

Logarithmi.
,,,
Num.
absolu.

,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,
,,
,,,

,,,

,,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,,
,,,

,,


,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,


,,
,,
,,
,,,
,,,
,,
,,

,,,

,,
,,,

,,
,,

,,,
,,
,,
,,,

,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,
,,,
,,,

,,


,,
,,
,,
,,,
,,,
,,
,,


,,
,,
,,,
,,,

,,

,,,
,,
,,


,,
,,
,,,
,,
,,
,,

,,,

,,

,,
,,
,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
Logarithmi.
,,
,,
,,

,,,

,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
,,
,,,
,,,
Num.
absolu.

,,
,,

Logarithmi.
,,

,,,
,,

190
Briggs’ 1624 table of logarithms (reconstruction, D. Roegel, 2010)
Chilias decimasexta.
Num.
absolu.

Logarithmi.
,,,
Num.
absolu.

,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,
,,
,,,

,,,

,,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,,
,,,

,,


,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,


,,
,,
,,
,,,
,,,
,,
,,

,,,

,,
,,,

,,
,,

,,,
,,
,,
,,,

,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,
,,,
,,,

,,


,,
,,
,,
,,,
,,,
,,
,,


,,
,,
,,,
,,,

,,

,,,
,,
,,


,,
,,
,,,
,,
,,
,,

,,,

,,

,,
,,
,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
Logarithmi.
,,
,,
,,

,,,

,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
,,
,,,
,,,
Num.
absolu.

,,
,,

Logarithmi.
,,

,,,
,,

191
Briggs’ 1624 table of logarithms (reconstruction, D. Roegel, 2010)
Chilias decimasexta.
Num.
absolu.

Logarithmi.
,,,
Num.
absolu.

,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,
,,
,,,

,,,

,,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,,
,,,

,,


,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,


,,
,,
,,
,,,
,,,
,,
,,

,,,

,,
,,,

,,
,,

,,,
,,
,,
,,,

,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,
,,,
,,,

,,


,,
,,
,,
,,,
,,,
,,
,,


,,
,,
,,,
,,,

,,

,,,
,,
,,


,,
,,
,,,
,,
,,
,,

,,,

,,

,,
,,
,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
Logarithmi.
,,
,,
,,

,,,

,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
,,
,,,
,,,
Num.
absolu.

,,
,,

Logarithmi.
,,

,,,
,,

192
Briggs’ 1624 table of logarithms (reconstruction, D. Roegel, 2010)
Chilias decimasexta.
Num.
absolu.

Logarithmi.
,,,
Num.
absolu.

,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,
,,
,,,

,,,

,,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,,
,,,

,,


,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,


,,
,,
,,
,,,
,,,
,,
,,

,,,

,,
,,,

,,
,,

,,,
,,
,,
,,,

,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,
,,,
,,,

,,


,,
,,
,,
,,,
,,,
,,
,,


,,
,,
,,,
,,,

,,

,,,
,,
,,


,,
,,
,,,
,,
,,
,,

,,,

,,

,,
,,
,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
Logarithmi.
,,
,,
,,

,,,

,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
,,
,,,
,,,
Num.
absolu.

,,
,,

Logarithmi.
,,

,,,
,,

193
Briggs’ 1624 table of logarithms (reconstruction, D. Roegel, 2010)
Chilias decimasexta.
Num.
absolu.

Logarithmi.
,,,
Num.
absolu.

,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,
,,
,,,

,,,

,,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,,
,,,

,,


,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,


,,
,,
,,
,,,
,,,
,,
,,

,,,

,,
,,,

,,
,,

,,,
,,
,,
,,,

,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,
,,,
,,,

,,


,,
,,
,,
,,,
,,,
,,
,,


,,
,,
,,,
,,,

,,

,,,
,,
,,


,,
,,
,,,
,,
,,
,,

,,,

,,

,,
,,
,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
Logarithmi.
,,
,,
,,

,,,

,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
,,
,,,
,,,
Num.
absolu.

,,
,,

Logarithmi.
,,

,,,
,,

194
Briggs’ 1624 table of logarithms (reconstruction, D. Roegel, 2010)
Chilias decimaseptima.
Num.
absolu.

Logarithmi.
,,,
Num.
absolu.

,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,
,,
,,,

,,,

,,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,,
,,,

,,


,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,


,,
,,
,,
,,,
,,,
,,
,,

,,,

,,
,,,

,,
,,

,,,
,,
,,
,,,

,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,
,,,
,,,

,,


,,
,,
,,
,,,
,,,
,,
,,


,,
,,
,,,
,,,

,,

,,,
,,
,,


,,
,,
,,,
,,
,,
,,

,,,

,,

,,
,,
,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
Logarithmi.
,,
,,
,,

,,,

,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
,,
,,,
,,,
Num.
absolu.

,,
,,

Logarithmi.
,,

,,,
,,

195
Briggs’ 1624 table of logarithms (reconstruction, D. Roegel, 2010)
Chilias decimaseptima.
Num.
absolu.

Logarithmi.
,,,
Num.
absolu.

,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,
,,
,,,

,,,

,,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,,
,,,

,,


,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,


,,
,,
,,
,,,
,,,
,,
,,

,,,

,,
,,,

,,
,,

,,,
,,
,,
,,,

,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,
,,,
,,,

,,


,,
,,
,,
,,,
,,,
,,
,,


,,
,,
,,,
,,,

,,

,,,
,,
,,


,,
,,
,,,
,,
,,
,,

,,,

,,

,,
,,
,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
Logarithmi.
,,
,,
,,

,,,

,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
,,
,,,
,,,
Num.
absolu.

,,
,,

Logarithmi.
,,

,,,
,,

196
Briggs’ 1624 table of logarithms (reconstruction, D. Roegel, 2010)
Chilias decimaseptima.
Num.
absolu.

Logarithmi.
,,,
Num.
absolu.

,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,
,,
,,,

,,,

,,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,,
,,,

,,


,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,


,,
,,
,,
,,,
,,,
,,
,,

,,,

,,
,,,

,,
,,

,,,
,,
,,
,,,

,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,
,,,
,,,

,,


,,
,,
,,
,,,
,,,
,,
,,


,,
,,
,,,
,,,

,,

,,,
,,
,,


,,
,,
,,,
,,
,,
,,

,,,

,,

,,
,,
,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
Logarithmi.
,,
,,
,,

,,,

,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
,,
,,,
,,,
Num.
absolu.

,,
,,

Logarithmi.
,,

,,,
,,

197
Briggs’ 1624 table of logarithms (reconstruction, D. Roegel, 2010)
Chilias decimaseptima.
Num.
absolu.

Logarithmi.
,,,
Num.
absolu.

,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,
,,
,,,

,,,

,,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,,
,,,

,,


,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,


,,
,,
,,
,,,
,,,
,,
,,

,,,

,,
,,,

,,
,,

,,,
,,
,,
,,,

,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,
,,,
,,,

,,


,,
,,
,,
,,,
,,,
,,
,,


,,
,,
,,,
,,,

,,

,,,
,,
,,


,,
,,
,,,
,,
,,
,,

,,,

,,

,,
,,
,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
Logarithmi.
,,
,,
,,

,,,

,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
,,
,,,
,,,
Num.
absolu.

,,
,,

Logarithmi.
,,

,,,
,,

198
Briggs’ 1624 table of logarithms (reconstruction, D. Roegel, 2010)
Chilias decimaseptima.
Num.
absolu.

Logarithmi.
,,,
Num.
absolu.

,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,
,,
,,,

,,,

,,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,,
,,,

,,


,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,


,,
,,
,,
,,,
,,,
,,
,,

,,,

,,
,,,

,,
,,

,,,
,,
,,
,,,

,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,
,,,
,,,

,,


,,
,,
,,
,,,
,,,
,,
,,


,,
,,
,,,
,,,

,,

,,,
,,
,,


,,
,,
,,,
,,
,,
,,

,,,

,,

,,
,,
,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
Logarithmi.
,,
,,
,,

,,,

,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
,,
,,,
,,,
Num.
absolu.

,,
,,

Logarithmi.
,,

,,,
,,

199
Briggs’ 1624 table of logarithms (reconstruction, D. Roegel, 2010)
Chilias decimaseptima.
Num.
absolu.

Logarithmi.
,,,
Num.
absolu.

,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,
,,
,,,

,,,

,,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,,
,,,

,,


,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,


,,
,,
,,
,,,
,,,
,,
,,

,,,

,,
,,,

,,
,,

,,,
,,
,,
,,,

,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,
,,,
,,,

,,


,,
,,
,,
,,,
,,,
,,
,,


,,
,,
,,,
,,,

,,

,,,
,,
,,


,,
,,
,,,
,,
,,
,,

,,,

,,

,,
,,
,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
Logarithmi.
,,
,,
,,

,,,

,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
,,
,,,
,,,
Num.
absolu.

,,
,,

Logarithmi.
,,

,,,
,,

200
Briggs’ 1624 table of logarithms (reconstruction, D. Roegel, 2010)
Chilias decimaseptima.
Num.
absolu.

Logarithmi.
,,,
Num.
absolu.

,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,
,,
,,,

,,,

,,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,,
,,,

,,


,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,


,,
,,
,,
,,,
,,,
,,
,,

,,,

,,
,,,

,,
,,

,,,
,,
,,
,,,

,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,
,,,
,,,

,,


,,
,,
,,
,,,
,,,
,,
,,


,,
,,
,,,
,,,

,,

,,,
,,
,,


,,
,,
,,,
,,
,,
,,

,,,

,,

,,
,,
,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
Logarithmi.
,,
,,
,,

,,,

,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
,,
,,,
,,,
Num.
absolu.

,,
,,

Logarithmi.
,,

,,,
,,

201
Briggs’ 1624 table of logarithms (reconstruction, D. Roegel, 2010)
Chilias decimaseptima.
Num.
absolu.

Logarithmi.
,,,
Num.
absolu.

,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,
,,
,,,

,,,

,,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,,
,,,

,,


,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,


,,
,,
,,
,,,
,,,
,,
,,

,,,

,,
,,,

,,
,,

,,,
,,
,,
,,,

,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,
,,,
,,,

,,


,,
,,
,,
,,,
,,,
,,
,,


,,
,,
,,,
,,,

,,

,,,
,,
,,


,,
,,
,,,
,,
,,
,,

,,,

,,

,,
,,
,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
Logarithmi.
,,
,,
,,

,,,

,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
,,
,,,
,,,
Num.
absolu.

,,
,,

Logarithmi.
,,

,,,
,,

202
Briggs’ 1624 table of logarithms (reconstruction, D. Roegel, 2010)
Chilias decimaseptima.
Num.
absolu.

Logarithmi.
,,,
Num.
absolu.

,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,
,,
,,,

,,,

,,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,,
,,,

,,


,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,


,,
,,
,,
,,,
,,,
,,
,,

,,,

,,
,,,

,,
,,

,,,
,,
,,
,,,

,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,
,,,
,,,

,,


,,
,,
,,
,,,
,,,
,,
,,


,,
,,
,,,
,,,

,,

,,,
,,
,,


,,
,,
,,,
,,
,,
,,

,,,

,,

,,
,,
,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
Logarithmi.
,,
,,
,,

,,,

,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
,,
,,,
,,,
Num.
absolu.

,,
,,

Logarithmi.
,,

,,,
,,

203
Briggs’ 1624 table of logarithms (reconstruction, D. Roegel, 2010)
Chilias decimaseptima.
Num.
absolu.

Logarithmi.
,,,
Num.
absolu.

,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,
,,
,,,

,,,

,,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,,
,,,

,,


,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,


,,
,,
,,
,,,
,,,
,,
,,

,,,

,,
,,,

,,
,,

,,,
,,
,,
,,,

,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,
,,,
,,,

,,


,,
,,
,,
,,,
,,,
,,
,,


,,
,,
,,,
,,,

,,

,,,
,,
,,


,,
,,
,,,
,,
,,
,,

,,,

,,

,,
,,
,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
Logarithmi.
,,
,,
,,

,,,

,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
,,
,,,
,,,
Num.
absolu.

,,
,,

Logarithmi.
,,

,,,
,,

204
Briggs’ 1624 table of logarithms (reconstruction, D. Roegel, 2010)
Chilias decimaoctaua.
Num.
absolu.

Logarithmi.
,,,
Num.
absolu.

,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,
,,
,,,

,,,

,,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,,
,,,

,,


,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,


,,
,,
,,
,,,
,,,
,,
,,

,,,

,,
,,,

,,
,,

,,,
,,
,,
,,,

,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,
,,,
,,,

,,


,,
,,
,,
,,,
,,,
,,
,,


,,
,,
,,,
,,,

,,

,,,
,,
,,


,,
,,
,,,
,,
,,
,,

,,,

,,

,,
,,
,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
Logarithmi.
,,
,,
,,

,,,

,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
,,
,,,
,,,
Num.
absolu.

,,
,,

Logarithmi.
,,

,,,
,,

205
Briggs’ 1624 table of logarithms (reconstruction, D. Roegel, 2010)
Chilias decimaoctaua.
Num.
absolu.

Logarithmi.
,,,
Num.
absolu.

,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,
,,
,,,

,,,

,,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,,
,,,

,,


,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,


,,
,,
,,
,,,
,,,
,,
,,

,,,

,,
,,,

,,
,,

,,,
,,
,,
,,,

,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,
,,,
,,,

,,


,,
,,
,,
,,,
,,,
,,
,,


,,
,,
,,,
,,,

,,

,,,
,,
,,


,,
,,
,,,
,,
,,
,,

,,,

,,

,,
,,
,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
Logarithmi.
,,
,,
,,

,,,

,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
,,
,,,
,,,
Num.
absolu.

,,
,,

Logarithmi.
,,

,,,
,,

206
Briggs’ 1624 table of logarithms (reconstruction, D. Roegel, 2010)
Chilias decimaoctaua.
Num.
absolu.

Logarithmi.
,,,
Num.
absolu.

,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,
,,
,,,

,,,

,,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,,
,,,

,,


,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,


,,
,,
,,
,,,
,,,
,,
,,

,,,

,,
,,,

,,
,,

,,,
,,
,,
,,,

,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,
,,,
,,,

,,


,,
,,
,,
,,,
,,,
,,
,,


,,
,,
,,,
,,,

,,

,,,
,,
,,


,,
,,
,,,
,,
,,
,,

,,,

,,

,,
,,
,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
Logarithmi.
,,
,,
,,

,,,

,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
,,
,,,
,,,
Num.
absolu.

,,
,,

Logarithmi.
,,

,,,
,,

207
Briggs’ 1624 table of logarithms (reconstruction, D. Roegel, 2010)
Chilias decimaoctaua.
Num.
absolu.

Logarithmi.
,,,
Num.
absolu.

,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,
,,
,,,

,,,

,,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,,
,,,

,,


,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,


,,
,,
,,
,,,
,,,
,,
,,

,,,

,,
,,,

,,
,,

,,,
,,
,,
,,,

,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,
,,,
,,,

,,


,,
,,
,,
,,,
,,,
,,
,,


,,
,,
,,,
,,,

,,

,,,
,,
,,


,,
,,
,,,
,,
,,
,,

,,,

,,

,,
,,
,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
Logarithmi.
,,
,,
,,

,,,

,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
,,
,,,
,,,
Num.
absolu.

,,
,,

Logarithmi.
,,

,,,
,,

208
Briggs’ 1624 table of logarithms (reconstruction, D. Roegel, 2010)
Chilias decimaoctaua.
Num.
absolu.

Logarithmi.
,,,
Num.
absolu.

,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,
,,
,,,

,,,

,,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,,
,,,

,,


,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,


,,
,,
,,
,,,
,,,
,,
,,

,,,

,,
,,,

,,
,,

,,,
,,
,,
,,,

,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,
,,,
,,,

,,


,,
,,
,,
,,,
,,,
,,
,,


,,
,,
,,,
,,,

,,

,,,
,,
,,


,,
,,
,,,
,,
,,
,,

,,,

,,

,,
,,
,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
Logarithmi.
,,
,,
,,

,,,

,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
,,
,,,
,,,
Num.
absolu.

,,
,,

Logarithmi.
,,

,,,
,,

209
Briggs’ 1624 table of logarithms (reconstruction, D. Roegel, 2010)
Chilias decimaoctaua.
Num.
absolu.

Logarithmi.
,,,
Num.
absolu.

,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,
,,
,,,

,,,

,,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,,
,,,

,,


,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,


,,
,,
,,
,,,
,,,
,,
,,

,,,

,,
,,,

,,
,,

,,,
,,
,,
,,,

,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,
,,,
,,,

,,


,,
,,
,,
,,,
,,,
,,
,,


,,
,,
,,,
,,,

,,

,,,
,,
,,


,,
,,
,,,
,,
,,
,,

,,,

,,

,,
,,
,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
Logarithmi.
,,
,,
,,

,,,

,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
,,
,,,
,,,
Num.
absolu.

,,
,,

Logarithmi.
,,

,,,
,,

210
Briggs’ 1624 table of logarithms (reconstruction, D. Roegel, 2010)
Chilias decimaoctaua.
Num.
absolu.

Logarithmi.
,,,
Num.
absolu.

,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,
,,
,,,

,,,

,,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,,
,,,

,,


,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,


,,
,,
,,
,,,
,,,
,,
,,

,,,

,,
,,,

,,
,,

,,,
,,
,,
,,,

,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,
,,,
,,,

,,


,,
,,
,,
,,,
,,,
,,
,,


,,
,,
,,,
,,,

,,

,,,
,,
,,


,,
,,
,,,
,,
,,
,,

,,,

,,

,,
,,
,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
Logarithmi.
,,
,,
,,

,,,

,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
,,
,,,
,,,
Num.
absolu.

,,
,,

Logarithmi.
,,

,,,
,,

211
Briggs’ 1624 table of logarithms (reconstruction, D. Roegel, 2010)
Chilias decimaoctaua.
Num.
absolu.

Logarithmi.
,,,
Num.
absolu.

,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,
,,
,,,

,,,

,,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,,
,,,

,,


,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,


,,
,,
,,
,,,
,,,
,,
,,

,,,

,,
,,,

,,
,,

,,,
,,
,,
,,,

,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,
,,,
,,,

,,


,,
,,
,,
,,,
,,,
,,
,,


,,
,,
,,,
,,,

,,

,,,
,,
,,


,,
,,
,,,
,,
,,
,,

,,,

,,

,,
,,
,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
Logarithmi.
,,
,,
,,

,,,

,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
,,
,,,
,,,
Num.
absolu.

,,
,,

Logarithmi.
,,

,,,
,,

212
Briggs’ 1624 table of logarithms (reconstruction, D. Roegel, 2010)
Chilias decimaoctaua.
Num.
absolu.

Logarithmi.
,,,
Num.
absolu.

,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,
,,
,,,

,,,

,,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,,
,,,

,,


,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,


,,
,,
,,
,,,
,,,
,,
,,

,,,

,,
,,,

,,
,,

,,,
,,
,,
,,,

,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,
,,,
,,,

,,


,,
,,
,,
,,,
,,,
,,
,,


,,
,,
,,,
,,,

,,

,,,
,,
,,


,,
,,
,,,
,,
,,
,,

,,,

,,

,,
,,
,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
Logarithmi.
,,
,,
,,

,,,

,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
,,
,,,
,,,
Num.
absolu.

,,
,,

Logarithmi.
,,

,,,
,,

213
Briggs’ 1624 table of logarithms (reconstruction, D. Roegel, 2010)
Chilias decimaoctaua.
Num.
absolu.

Logarithmi.
,,,
Num.
absolu.

,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,
,,
,,,

,,,

,,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,,
,,,

,,


,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,


,,
,,
,,
,,,
,,,
,,
,,

,,,

,,
,,,

,,
,,

,,,
,,
,,
,,,

,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,
,,,
,,,

,,


,,
,,
,,
,,,
,,,
,,
,,


,,
,,
,,,
,,,

,,

,,,
,,
,,


,,
,,
,,,
,,
,,
,,

,,,

,,

,,
,,
,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
Logarithmi.
,,
,,
,,

,,,

,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
,,
,,,
,,,
Num.
absolu.

,,
,,

Logarithmi.
,,

,,,
,,

214
Briggs’ 1624 table of logarithms (reconstruction, D. Roegel, 2010)
Chilias decimanona.
Num.
absolu.

Logarithmi.
,,,
Num.
absolu.

,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,
,,
,,,

,,,

,,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,,
,,,

,,


,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,


,,
,,
,,
,,,
,,,
,,
,,

,,,

,,
,,,

,,
,,

,,,
,,
,,
,,,

,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,
,,,
,,,

,,


,,
,,
,,
,,,
,,,
,,
,,


,,
,,
,,,
,,,

,,

,,,
,,
,,


,,
,,
,,,
,,
,,
,,

,,,

,,

,,
,,
,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
Logarithmi.
,,
,,
,,

,,,

,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
,,
,,,
,,,
Num.
absolu.

,,
,,

Logarithmi.
,,

,,,
,,

215
Briggs’ 1624 table of logarithms (reconstruction, D. Roegel, 2010)
Chilias decimanona.
Num.
absolu.

Logarithmi.
,,,
Num.
absolu.

,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,
,,
,,,

,,,

,,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,,
,,,

,,


,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,


,,
,,
,,
,,,
,,,
,,
,,

,,,

,,
,,,

,,
,,

,,,
,,
,,
,,,

,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,
,,,
,,,

,,


,,
,,
,,
,,,
,,,
,,
,,


,,
,,
,,,
,,,

,,

,,,
,,
,,


,,
,,
,,,
,,
,,
,,

,,,

,,

,,
,,
,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
Logarithmi.
,,
,,
,,

,,,

,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
,,
,,,
,,,
Num.
absolu.

,,
,,

Logarithmi.
,,

,,,
,,

216
Briggs’ 1624 table of logarithms (reconstruction, D. Roegel, 2010)
Chilias decimanona.
Num.
absolu.

Logarithmi.
,,,
Num.
absolu.

,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,
,,
,,,

,,,

,,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,,
,,,

,,


,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,


,,
,,
,,
,,,
,,,
,,
,,

,,,

,,
,,,

,,
,,

,,,
,,
,,
,,,

,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,
,,,
,,,

,,


,,
,,
,,
,,,
,,,
,,
,,


,,
,,
,,,
,,,

,,

,,,
,,
,,


,,
,,
,,,
,,
,,
,,

,,,

,,

,,
,,
,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
Logarithmi.
,,
,,
,,

,,,

,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
,,
,,,
,,,
Num.
absolu.

,,
,,

Logarithmi.
,,

,,,
,,

217
Briggs’ 1624 table of logarithms (reconstruction, D. Roegel, 2010)
Chilias decimanona.
Num.
absolu.

Logarithmi.
,,,
Num.
absolu.

,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,
,,
,,,

,,,

,,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,,
,,,

,,


,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,


,,
,,
,,
,,,
,,,
,,
,,

,,,

,,
,,,

,,
,,

,,,
,,
,,
,,,

,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,
,,,
,,,

,,


,,
,,
,,
,,,
,,,
,,
,,


,,
,,
,,,
,,,

,,

,,,
,,
,,


,,
,,
,,,
,,
,,
,,

,,,

,,

,,
,,
,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
Logarithmi.
,,
,,
,,

,,,

,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
,,
,,,
,,,
Num.
absolu.

,,
,,

Logarithmi.
,,

,,,
,,

218
Briggs’ 1624 table of logarithms (reconstruction, D. Roegel, 2010)
Chilias decimanona.
Num.
absolu.

Logarithmi.
,,,
Num.
absolu.

,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,
,,
,,,

,,,

,,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,,
,,,

,,


,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,


,,
,,
,,
,,,
,,,
,,
,,

,,,

,,
,,,

,,
,,

,,,
,,
,,
,,,

,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,
,,,
,,,

,,


,,
,,
,,
,,,
,,,
,,
,,


,,
,,
,,,
,,,

,,

,,,
,,
,,


,,
,,
,,,
,,
,,
,,

,,,

,,

,,
,,
,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
Logarithmi.
,,
,,
,,

,,,

,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
,,
,,,
,,,
Num.
absolu.

,,
,,

Logarithmi.
,,

,,,
,,

219
Briggs’ 1624 table of logarithms (reconstruction, D. Roegel, 2010)
Chilias decimanona.
Num.
absolu.

Logarithmi.
,,,
Num.
absolu.

,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,
,,
,,,

,,,

,,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,,
,,,

,,


,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,


,,
,,
,,
,,,
,,,
,,
,,

,,,

,,
,,,

,,
,,

,,,
,,
,,
,,,

,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,
,,,
,,,

,,


,,
,,
,,
,,,
,,,
,,
,,


,,
,,
,,,
,,,

,,

,,,
,,
,,


,,
,,
,,,
,,
,,
,,

,,,

,,

,,
,,
,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
Logarithmi.
,,
,,
,,

,,,

,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
,,
,,,
,,,
Num.
absolu.

,,
,,

Logarithmi.
,,

,,,
,,

220
Briggs’ 1624 table of logarithms (reconstruction, D. Roegel, 2010)
Chilias decimanona.
Num.
absolu.

Logarithmi.
,,,
Num.
absolu.

,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,
,,
,,,

,,,

,,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,,
,,,

,,


,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,


,,
,,
,,
,,,
,,,
,,
,,

,,,

,,
,,,

,,
,,

,,,
,,
,,
,,,

,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,
,,,
,,,

,,


,,
,,
,,
,,,
,,,
,,
,,


,,
,,
,,,
,,,

,,

,,,
,,
,,


,,
,,
,,,
,,
,,
,,

,,,

,,

,,
,,
,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
Logarithmi.
,,
,,
,,

,,,

,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
,,
,,,
,,,
Num.
absolu.

,,
,,

Logarithmi.
,,

,,,
,,

221
Briggs’ 1624 table of logarithms (reconstruction, D. Roegel, 2010)
Chilias decimanona.
Num.
absolu.

Logarithmi.
,,,
Num.
absolu.

,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,
,,
,,,

,,,

,,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,,
,,,

,,


,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,


,,
,,
,,
,,,
,,,
,,
,,

,,,

,,
,,,

,,
,,

,,,
,,
,,
,,,

,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,
,,,
,,,

,,


,,
,,
,,
,,,
,,,
,,
,,


,,
,,
,,,
,,,

,,

,,,
,,
,,


,,
,,
,,,
,,
,,
,,

,,,

,,

,,
,,
,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
Logarithmi.
,,
,,
,,

,,,

,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
,,
,,,
,,,
Num.
absolu.

,,
,,

Logarithmi.
,,

,,,
,,

222
Briggs’ 1624 table of logarithms (reconstruction, D. Roegel, 2010)
Chilias decimanona.
Num.
absolu.

Logarithmi.
,,,
Num.
absolu.

,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,
,,
,,,

,,,

,,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,,
,,,

,,


,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,


,,
,,
,,
,,,
,,,
,,
,,

,,,

,,
,,,

,,
,,

,,,
,,
,,
,,,

,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,
,,,
,,,

,,


,,
,,
,,
,,,
,,,
,,
,,


,,
,,
,,,
,,,

,,

,,,
,,
,,


,,
,,
,,,
,,
,,
,,

,,,

,,

,,
,,
,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
Logarithmi.
,,
,,
,,

,,,

,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
,,
,,,
,,,
Num.
absolu.

,,
,,

Logarithmi.
,,

,,,
,,

223
Briggs’ 1624 table of logarithms (reconstruction, D. Roegel, 2010)
Chilias decimanona.
Num.
absolu.

Logarithmi.
,,,
Num.
absolu.

,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,
,,
,,,

,,,

,,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,,
,,,

,,


,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,


,,
,,
,,
,,,
,,,
,,
,,

,,,

,,
,,,

,,
,,

,,,
,,
,,
,,,

,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,
,,,
,,,

,,


,,
,,
,,
,,,
,,,
,,
,,


,,
,,
,,,
,,,

,,

,,,
,,
,,


,,
,,
,,,
,,
,,
,,

,,,

,,

,,
,,
,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
Logarithmi.
,,
,,
,,

,,,

,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
,,
,,,
,,,
Num.
absolu.

,,
,,

Logarithmi.
,,

,,,
,,

224
Briggs’ 1624 table of logarithms (reconstruction, D. Roegel, 2010)
Chilias vicesima.
Num.
absolu.

Logarithmi.
,,,
Num.
absolu.

,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,
,,
,,,

,,,

,,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,,
,,,

,,


,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,


,,
,,
,,
,,,
,,,
,,
,,

,,,

,,
,,,

,,
,,

,,,
,,
,,
,,,

,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,
,,,
,,,

,,


,,
,,
,,
,,,
,,,
,,
,,


,,
,,
,,,
,,,

,,

,,,
,,
,,


,,
,,
,,,
,,
,,
,,

,,,

,,

,,
,,
,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
Logarithmi.
,,
,,
,,

,,,

,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
,,
,,,
,,,
Num.
absolu.

,,
,,

Logarithmi.
,,

,,,
,,

225
Briggs’ 1624 table of logarithms (reconstruction, D. Roegel, 2010)
Chilias vicesima.
Num.
absolu.

Logarithmi.
,,,
Num.
absolu.

,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,
,,
,,,

,,,

,,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,,
,,,

,,


,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,


,,
,,
,,
,,,
,,,
,,
,,

,,,

,,
,,,

,,
,,

,,,
,,
,,
,,,

,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,
,,,
,,,

,,


,,
,,
,,
,,,
,,,
,,
,,


,,
,,
,,,
,,,

,,

,,,
,,
,,


,,
,,
,,,
,,
,,
,,

,,,

,,

,,
,,
,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
Logarithmi.
,,
,,
,,

,,,

,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
,,
,,,
,,,
Num.
absolu.

,,
,,

Logarithmi.
,,

,,,
,,

226
Briggs’ 1624 table of logarithms (reconstruction, D. Roegel, 2010)
Chilias vicesima.
Num.
absolu.

Logarithmi.
,,,
Num.
absolu.

,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,
,,
,,,

,,,

,,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,,
,,,

,,


,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,


,,
,,
,,
,,,
,,,
,,
,,

,,,

,,
,,,

,,
,,

,,,
,,
,,
,,,

,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,
,,,
,,,

,,


,,
,,
,,
,,,
,,,
,,
,,


,,
,,
,,,
,,,

,,

,,,
,,
,,


,,
,,
,,,
,,
,,
,,

,,,

,,

,,
,,
,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
Logarithmi.
,,
,,
,,

,,,

,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
,,
,,,
,,,
Num.
absolu.

,,
,,

Logarithmi.
,,

,,,
,,

227
Briggs’ 1624 table of logarithms (reconstruction, D. Roegel, 2010)
Chilias vicesima.
Num.
absolu.

Logarithmi.
,,,
Num.
absolu.

,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,
,,
,,,

,,,

,,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,,
,,,

,,


,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,


,,
,,
,,
,,,
,,,
,,
,,

,,,

,,
,,,

,,
,,

,,,
,,
,,
,,,

,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,
,,,
,,,

,,


,,
,,
,,
,,,
,,,
,,
,,


,,
,,
,,,
,,,

,,

,,,
,,
,,


,,
,,
,,,
,,
,,
,,

,,,

,,

,,
,,
,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
Logarithmi.
,,
,,
,,

,,,

,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
,,
,,,
,,,
Num.
absolu.

,,
,,

Logarithmi.
,,

,,,
,,

228
Briggs’ 1624 table of logarithms (reconstruction, D. Roegel, 2010)
Chilias vicesima.
Num.
absolu.

Logarithmi.
,,,
Num.
absolu.

,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,
,,
,,,

,,,

,,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,,
,,,

,,


,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,


,,
,,
,,
,,,
,,,
,,
,,

,,,

,,
,,,

,,
,,

,,,
,,
,,
,,,

,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,
,,,
,,,

,,


,,
,,
,,
,,,
,,,
,,
,,


,,
,,
,,,
,,,

,,

,,,
,,
,,


,,
,,
,,,
,,
,,
,,

,,,

,,

,,
,,
,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
Logarithmi.
,,
,,
,,

,,,

,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
,,
,,,
,,,
Num.
absolu.

,,
,,

Logarithmi.
,,

,,,
,,

229
Briggs’ 1624 table of logarithms (reconstruction, D. Roegel, 2010)
Chilias vicesima.
Num.
absolu.

Logarithmi.
,,,
Num.
absolu.

,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,
,,
,,,

,,,

,,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,,
,,,

,,


,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,


,,
,,
,,
,,,
,,,
,,
,,

,,,

,,
,,,

,,
,,

,,,
,,
,,
,,,

,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,
,,,
,,,

,,


,,
,,
,,
,,,
,,,
,,
,,


,,
,,
,,,
,,,

,,

,,,
,,
,,


,,
,,
,,,
,,
,,
,,

,,,

,,

,,
,,
,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
Logarithmi.
,,
,,
,,

,,,

,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
,,
,,,
,,,
Num.
absolu.

,,
,,

Logarithmi.
,,

,,,
,,

230
Briggs’ 1624 table of logarithms (reconstruction, D. Roegel, 2010)
Chilias vicesima.
Num.
absolu.

Logarithmi.
,,,
Num.
absolu.

,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,
,,
,,,

,,,

,,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,,
,,,

,,


,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,


,,
,,
,,
,,,
,,,
,,
,,

,,,

,,
,,,

,,
,,

,,,
,,
,,
,,,

,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,
,,,
,,,

,,


,,
,,
,,
,,,
,,,
,,
,,


,,
,,
,,,
,,,

,,

,,,
,,
,,


,,
,,
,,,
,,
,,
,,

,,,

,,

,,
,,
,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
Logarithmi.
,,
,,
,,

,,,

,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
,,
,,,
,,,
Num.
absolu.

,,
,,

Logarithmi.
,,

,,,
,,

231
Briggs’ 1624 table of logarithms (reconstruction, D. Roegel, 2010)
Chilias vicesima.
Num.
absolu.

Logarithmi.
,,,
Num.
absolu.

,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,
,,
,,,

,,,

,,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,,
,,,

,,


,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,


,,
,,
,,
,,,
,,,
,,
,,

,,,

,,
,,,

,,
,,

,,,
,,
,,
,,,

,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,
,,,
,,,

,,


,,
,,
,,
,,,
,,,
,,
,,


,,
,,
,,,
,,,

,,

,,,
,,
,,


,,
,,
,,,
,,
,,
,,

,,,

,,

,,
,,
,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
Logarithmi.
,,
,,
,,

,,,

,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
,,
,,,
,,,
Num.
absolu.

,,
,,

Logarithmi.
,,

,,,
,,

232
Briggs’ 1624 table of logarithms (reconstruction, D. Roegel, 2010)
Chilias vicesima.
Num.
absolu.

Logarithmi.
,,,
Num.
absolu.

,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,
,,
,,,

,,,

,,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,,
,,,

,,


,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,


,,
,,
,,
,,,
,,,
,,
,,

,,,

,,
,,,

,,
,,

,,,
,,
,,
,,,

,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,
,,,
,,,

,,


,,
,,
,,
,,,
,,,
,,
,,


,,
,,
,,,
,,,

,,

,,,
,,
,,


,,
,,
,,,
,,
,,
,,

,,,

,,

,,
,,
,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
Logarithmi.
,,
,,
,,

,,,

,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
,,
,,,
,,,
Num.
absolu.

,,
,,

Logarithmi.
,,

,,,
,,

233
Briggs’ 1624 table of logarithms (reconstruction, D. Roegel, 2010)
Chilias vicesima.
Num.
absolu.

Logarithmi.
,,,
Num.
absolu.

,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,
,,
,,,

,,,

,,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,

,,,

,,,

,,,
,,
,,
,,
,,
,,
,,

,,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,

,,,
,,

,,,

,,,

,,,
,,

,,,

,,,
,,
,,
,,
,,,
,,,

,,


,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,


,,
,,
,,
,,,
,,,
,,
,,

,,,

,,
,,,

,,
,,

,,,
,,
,,
,,,

,,
,,

,,
,,
,,
,,,
,,
,,
,,

,,,
,,
,,
,,,
,,,

,,


,,
,,
,,
,,,
,,,
,,
,,


,,
,,
,,,
,,,

,,

,,,
,,
,,


,,
,,
,,,
,,
,,
,,

,,,

,,

,,
,,
,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
234
Logarithmi.
,,
,,
,,

,,,

,,
,,,
,,,
,,
,,


,,
,,

,,,
,,
,,
,,,
,,,
Num.
absolu.

,,
,,

Logarithmi.
,,

,,,
,,
Briggs’ 1624 table of logarithms (reconstruction, D. Roegel, 2010)
Chilias nonagesima prima.
Num.
absolu.

Logarithmi.
,,,
Num.
absolu.

Logarithmi.
,,,
,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,
,
,
,
,
,
,

,,,

,,,

,,,

,,,

,,,

,,,
,
,
,
,
,
,

,,,

,,,

,,,
,
,
,

,,,

,,,

,,,
,
,
,

,,,

,,,

,,,
,
,
,
,,,
,
,
,

,
,
,

,,,
,
,
,,,

,
,
,

,,,
,
,


,
,
,,,
,,,
,
,


,
,
,,,
,
,
,

,
,
,
,,,
,,,
,
,


,
,
,
,,,
,,,
,
,


,
,
,,,
,,,
,
,


,
,
,,,
,
,
,

,
,
,
,,,
,,,
,
,


,
,
,

,,,
,
,
,,,

,
,

,,,
,
,


,
,
,,,
,
,
,

,
,
,

,,,
,
,
,,,

,
,

,,,
,
,
Logarithmi.
,
,
,

,,,
,
,


,
,
,,,
,,,
,
,

Num.
absolu.

,

,,,
,

235
Briggs’ 1624 table of logarithms (reconstruction, D. Roegel, 2010)
Chilias nonagesima prima.
Num.
absolu.

Logarithmi.
,,,
Num.
absolu.

Logarithmi.
,,,
,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,
,
,
,
,
,
,

,,,

,,,

,,,

,,,

,,,

,,,
,
,
,
,
,
,

,,,

,,,

,,,
,
,
,

,,,

,,,

,,,
,
,
,

,,,

,,,

,,,
,
,
,
,,,
,
,
,

,
,
,

,,,
,
,
,,,

,
,
,

,,,
,
,


,
,
,,,
,,,
,
,


,
,
,,,
,
,
,

,
,
,
,,,
,,,
,
,


,
,
,
,,,
,,,
,
,


,
,
,,,
,,,
,
,


,
,
,,,
,
,
,

,
,
,
,,,
,,,
,
,


,
,
,

,,,
,
,
,,,

,
,

,,,
,
,


,
,
,,,
,
,
,

,
,
,

,,,
,
,
,,,

,
,

,,,
,
,
Logarithmi.
,
,
,

,,,
,
,


,
,
,,,
,,,
,
,

Num.
absolu.

,

,,,
,

236
Briggs’ 1624 table of logarithms (reconstruction, D. Roegel, 2010)
Chilias nonagesima prima.
Num.
absolu.

Logarithmi.
,,,
Num.
absolu.

Logarithmi.
,,,
,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,
,
,
,
,
,
,

,,,

,,,

,,,

,,,

,,,

,,,
,
,
,
,
,
,

,,,

,,,

,,,
,
,
,

,,,

,,,

,,,
,
,
,

,,,

,,,

,,,
,
,
,
,,,
,
,
,

,
,
,

,,,
,
,
,,,

,
,
,

,,,
,
,


,
,
,,,
,,,
,
,


,
,
,,,
,
,
,

,
,
,
,,,
,,,
,
,


,
,
,
,,,
,,,
,
,


,
,
,,,
,,,
,
,


,
,
,,,
,
,
,

,
,
,
,,,
,,,
,
,


,
,
,

,,,
,
,
,,,

,
,

,,,
,
,


,
,
,,,
,
,
,

,
,
,

,,,
,
,
,,,

,
,

,,,
,
,
Logarithmi.
,
,
,

,,,
,
,


,
,
,,,
,,,
,
,

Num.
absolu.

,

,,,
,

237
Briggs’ 1624 table of logarithms (reconstruction, D. Roegel, 2010)
Chilias nonagesima prima.
Num.
absolu.

Logarithmi.
,,,
Num.
absolu.

Logarithmi.
,,,
,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,
,
,
,
,
,
,

,,,

,,,

,,,

,,,

,,,

,,,
,
,
,
,
,
,

,,,

,,,

,,,
,
,
,

,,,

,,,

,,,
,
,
,

,,,

,,,

,,,
,
,
,
,,,
,
,
,

,
,
,

,,,
,
,
,,,

,
,
,

,,,
,
,


,
,
,,,
,,,
,
,


,
,
,,,
,
,
,

,
,
,
,,,
,,,
,
,


,
,
,
,,,
,,,
,
,


,
,
,,,
,,,
,
,


,
,
,,,
,
,
,

,
,
,
,,,
,,,
,
,


,
,
,

,,,
,
,
,,,

,
,

,,,
,
,


,
,
,,,
,
,
,

,
,
,

,,,
,
,
,,,

,
,

,,,
,
,
Logarithmi.
,
,
,

,,,
,
,


,
,
,,,
,,,
,
,

Num.
absolu.

,

,,,
,

238
Briggs’ 1624 table of logarithms (reconstruction, D. Roegel, 2010)
Chilias nonagesima prima.
Num.
absolu.

Logarithmi.
,,,
Num.
absolu.

Logarithmi.
,,,
,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,
,
,
,
,
,
,

,,,

,,,

,,,

,,,

,,,

,,,
,
,
,
,
,
,

,,,

,,,

,,,
,
,
,

,,,

,,,

,,,
,
,
,

,,,

,,,

,,,
,
,
,
,,,
,
,
,

,
,
,

,,,
,
,
,,,

,
,
,

,,,
,
,


,
,
,,,
,,,
,
,


,
,
,,,
,
,
,

,
,
,
,,,
,,,
,
,


,
,
,
,,,
,,,
,
,


,
,
,,,
,,,
,
,


,
,
,,,
,
,
,

,
,
,
,,,
,,,
,
,


,
,
,

,,,
,
,
,,,

,
,

,,,
,
,


,
,
,,,
,
,
,

,
,
,

,,,
,
,
,,,

,
,

,,,
,
,
Logarithmi.
,
,
,

,,,
,
,


,
,
,,,
,,,
,
,

Num.
absolu.

,

,,,
,

239
Briggs’ 1624 table of logarithms (reconstruction, D. Roegel, 2010)
Chilias nonagesima prima.
Num.
absolu.

Logarithmi.
,,,
Num.
absolu.

Logarithmi.
,,,
,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,
,
,
,
,
,
,

,,,

,,,

,,,

,,,

,,,

,,,
,
,
,
,
,
,

,,,

,,,

,,,
,
,
,

,,,

,,,

,,,
,
,
,

,,,

,,,

,,,
,
,
,
,,,
,
,
,

,
,
,

,,,
,
,
,,,

,
,
,

,,,
,
,


,
,
,,,
,,,
,
,


,
,
,,,
,
,
,

,
,
,
,,,
,,,
,
,


,
,
,
,,,
,,,
,
,


,
,
,,,
,,,
,
,


,
,
,,,
,
,
,

,
,
,
,,,
,,,
,
,


,
,
,

,,,
,
,
,,,

,
,

,,,
,
,


,
,
,,,
,
,
,

,
,
,

,,,
,
,
,,,

,
,

,,,
,
,
Logarithmi.
,
,
,

,,,
,
,


,
,
,,,
,,,
,
,

Num.
absolu.

,

,,,
,

240
Briggs’ 1624 table of logarithms (reconstruction, D. Roegel, 2010)
Chilias nonagesima prima.
Num.
absolu.

Logarithmi.
,,,
Num.
absolu.

Logarithmi.
,,,
,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,
,
,
,
,
,
,

,,,

,,,

,,,

,,,

,,,

,,,
,
,
,
,
,
,

,,,

,,,

,,,
,
,
,

,,,

,,,

,,,
,
,
,

,,,

,,,

,,,
,
,
,
,,,
,
,
,

,
,
,

,,,
,
,
,,,

,
,
,

,,,
,
,


,
,
,,,
,,,
,
,


,
,
,,,
,
,
,

,
,
,
,,,
,,,
,
,


,
,
,
,,,
,,,
,
,


,
,
,,,
,,,
,
,


,
,
,,,
,
,
,

,
,
,
,,,
,,,
,
,


,
,
,

,,,
,
,
,,,

,
,

,,,
,
,


,
,
,,,
,
,
,

,
,
,

,,,
,
,
,,,

,
,

,,,
,
,
Logarithmi.
,
,
,

,,,
,
,


,
,
,,,
,,,
,
,

Num.
absolu.

,

,,,
,

241
Briggs’ 1624 table of logarithms (reconstruction, D. Roegel, 2010)
Chilias nonagesima prima.
Num.
absolu.

Logarithmi.
,,,
Num.
absolu.

Logarithmi.
,,,
,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,
,
,
,
,
,
,

,,,

,,,

,,,

,,,

,,,

,,,
,
,
,
,
,
,

,,,

,,,

,,,
,
,
,

,,,

,,,

,,,
,
,
,

,,,

,,,

,,,
,
,
,
,,,
,
,
,

,
,
,

,,,
,
,
,,,

,
,
,

,,,
,
,


,
,
,,,
,,,
,
,


,
,
,,,
,
,
,

,
,
,
,,,
,,,
,
,


,
,
,
,,,
,,,
,
,


,
,
,,,
,,,
,
,


,
,
,,,
,
,
,

,
,
,
,,,
,,,
,
,


,
,
,

,,,
,
,
,,,

,
,

,,,
,
,


,
,
,,,
,
,
,

,
,
,

,,,
,
,
,,,

,
,

,,,
,
,
Logarithmi.
,
,
,

,,,
,
,


,
,
,,,
,,,
,
,

Num.
absolu.

,

,,,
,

242
Briggs’ 1624 table of logarithms (reconstruction, D. Roegel, 2010)
Chilias nonagesima prima.
Num.
absolu.

Logarithmi.
,,,
Num.
absolu.

Logarithmi.
,,,
,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,
,
,
,
,
,
,

,,,

,,,

,,,

,,,

,,,

,,,
,
,
,
,
,
,

,,,

,,,

,,,
,
,
,

,,,

,,,

,,,
,
,
,

,,,

,,,

,,,
,
,
,
,,,
,
,
,

,
,
,

,,,
,
,
,,,

,
,
,

,,,
,
,


,
,
,,,
,,,
,
,


,
,
,,,
,
,
,

,
,
,
,,,
,,,
,
,


,
,
,
,,,
,,,
,
,


,
,
,,,
,,,
,
,


,
,
,,,
,
,
,

,
,
,
,,,
,,,
,
,


,
,
,

,,,
,
,
,,,

,
,

,,,
,
,


,
,
,,,
,
,
,

,
,
,

,,,
,
,
,,,

,
,

,,,
,
,
Logarithmi.
,
,
,

,,,
,
,


,
,
,,,
,,,
,
,

Num.
absolu.

,

,,,
,

243
Briggs’ 1624 table of logarithms (reconstruction, D. Roegel, 2010)
Chilias nonagesima prima.
Num.
absolu.

Logarithmi.
,,,
Num.
absolu.

Logarithmi.
,,,
,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,
,
,
,
,
,
,

,,,

,,,

,,,

,,,

,,,

,,,
,
,
,
,
,
,

,,,

,,,

,,,
,
,
,

,,,

,,,

,,,
,
,
,

,,,

,,,

,,,
,
,
,
,,,
,
,
,

,
,
,

,,,
,
,
,,,

,
,
,

,,,
,
,


,
,
,,,
,,,
,
,


,
,
,,,
,
,
,

,
,
,
,,,
,,,
,
,


,
,
,
,,,
,,,
,
,


,
,
,,,
,,,
,
,


,
,
,,,
,
,
,

,
,
,
,,,
,,,
,
,


,
,
,

,,,
,
,
,,,

,
,

,,,
,
,


,
,
,,,
,
,
,

,
,
,

,,,
,
,
,,,

,
,

,,,
,
,
Logarithmi.
,
,
,

,,,
,
,


,
,
,,,
,,,
,
,

Num.
absolu.

,

,,,
,

244
Briggs’ 1624 table of logarithms (reconstruction, D. Roegel, 2010)
Chilias nonagesima secunda.
Num.
absolu.

Logarithmi.
,,,
Num.
absolu.

Logarithmi.
,,,
,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,
,
,
,
,
,
,

,,,

,,,

,,,

,,,

,,,

,,,
,
,
,
,
,
,

,,,

,,,

,,,
,
,
,

,,,

,,,

,,,
,
,
,

,,,

,,,

,,,
,
,
,
,,,
,
,
,

,
,
,

,,,
,
,
,,,

,
,
,

,,,
,
,


,
,
,,,
,,,
,
,


,
,
,,,
,
,
,

,
,
,
,,,
,,,
,
,


,
,
,
,,,
,,,
,
,


,
,
,,,
,,,
,
,


,
,
,,,
,
,
,

,
,
,
,,,
,,,
,
,


,
,
,

,,,
,
,
,,,

,
,

,,,
,
,


,
,
,,,
,
,
,

,
,
,

,,,
,
,
,,,

,
,

,,,
,
,
Logarithmi.
,
,
,

,,,
,
,


,
,
,,,
,,,
,
,

Num.
absolu.

,

,,,
,

245
Briggs’ 1624 table of logarithms (reconstruction, D. Roegel, 2010)
Chilias nonagesima secunda.
Num.
absolu.

Logarithmi.
,,,
Num.
absolu.

Logarithmi.
,,,
,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,
,
,
,
,
,
,

,,,

,,,

,,,

,,,

,,,

,,,
,
,
,
,
,
,

,,,

,,,

,,,
,
,
,

,,,

,,,

,,,
,
,
,

,,,

,,,

,,,
,
,
,
,,,
,
,
,

,
,
,

,,,
,
,
,,,

,
,
,

,,,
,
,


,
,
,,,
,,,
,
,


,
,
,,,
,
,
,

,
,
,
,,,
,,,
,
,


,
,
,
,,,
,,,
,
,


,
,
,,,
,,,
,
,


,
,
,,,
,
,
,

,
,
,
,,,
,,,
,
,


,
,
,

,,,
,
,
,,,

,
,

,,,
,
,


,
,
,,,
,
,
,

,
,
,

,,,
,
,
,,,

,
,

,,,
,
,
Logarithmi.
,
,
,

,,,
,
,


,
,
,,,
,,,
,
,

Num.
absolu.

,

,,,
,

246
Briggs’ 1624 table of logarithms (reconstruction, D. Roegel, 2010)
Chilias nonagesima secunda.
Num.
absolu.

Logarithmi.
,,,
Num.
absolu.

Logarithmi.
,,,
,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,
,
,
,
,
,
,

,,,

,,,

,,,

,,,

,,,

,,,
,
,
,
,
,
,

,,,

,,,

,,,
,
,
,

,,,

,,,

,,,
,
,
,

,,,

,,,

,,,
,
,
,
,,,
,
,
,

,
,
,

,,,
,
,
,,,

,
,
,

,,,
,
,


,
,
,,,
,,,
,
,


,
,
,,,
,
,
,

,
,
,
,,,
,,,
,
,


,
,
,
,,,
,,,
,
,


,
,
,,,
,,,
,
,


,
,
,,,
,
,
,

,
,
,
,,,
,,,
,
,


,
,
,

,,,
,
,
,,,

,
,

,,,
,
,


,
,
,,,
,
,
,

,
,
,

,,,
,
,
,,,

,
,

,,,
,
,
Logarithmi.
,
,
,

,,,
,
,


,
,
,,,
,,,
,
,

Num.
absolu.

,

,,,
,

247
Briggs’ 1624 table of logarithms (reconstruction, D. Roegel, 2010)
Chilias nonagesima secunda.
Num.
absolu.

Logarithmi.
,,,
Num.
absolu.

Logarithmi.
,,,
,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,
,
,
,
,
,
,

,,,

,,,

,,,

,,,

,,,

,,,
,
,
,
,
,
,

,,,

,,,

,,,
,
,
,

,,,

,,,

,,,
,
,
,

,,,

,,,

,,,
,
,
,
,,,
,
,
,

,
,
,

,,,
,
,
,,,

,
,
,

,,,
,
,


,
,
,,,
,,,
,
,


,
,
,,,
,
,
,

,
,
,
,,,
,,,
,
,


,
,
,
,,,
,,,
,
,


,
,
,,,
,,,
,
,


,
,
,,,
,
,
,

,
,
,
,,,
,,,
,
,


,
,
,

,,,
,
,
,,,

,
,

,,,
,
,


,
,
,,,
,
,
,

,
,
,

,,,
,
,
,,,

,
,

,,,
,
,
Logarithmi.
,
,
,

,,,
,
,


,
,
,,,
,,,
,
,

Num.
absolu.

,

,,,
,

248
Briggs’ 1624 table of logarithms (reconstruction, D. Roegel, 2010)
Chilias nonagesima secunda.
Num.
absolu.

Logarithmi.
,,,
Num.
absolu.

Logarithmi.
,,,
,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,
,
,
,
,
,
,

,,,

,,,

,,,

,,,

,,,

,,,
,
,
,
,
,
,

,,,

,,,

,,,
,
,
,

,,,

,,,

,,,
,
,
,

,,,

,,,

,,,
,
,
,
,,,
,
,
,

,
,
,

,,,
,
,
,,,

,
,
,

,,,
,
,


,
,
,,,
,,,
,
,


,
,
,,,
,
,
,

,
,
,
,,,
,,,
,
,


,
,
,
,,,
,,,
,
,


,
,
,,,
,,,
,
,


,
,
,,,
,
,
,

,
,
,
,,,
,,,
,
,


,
,
,

,,,
,
,
,,,

,
,

,,,
,
,


,
,
,,,
,
,
,

,
,
,

,,,
,
,
,,,

,
,

,,,
,
,
Logarithmi.
,
,
,

,,,
,
,


,
,
,,,
,,,
,
,

Num.
absolu.

,

,,,
,

249
Briggs’ 1624 table of logarithms (reconstruction, D. Roegel, 2010)
Chilias nonagesima secunda.
Num.
absolu.

Logarithmi.
,,,
Num.
absolu.

Logarithmi.
,,,
,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,
,
,
,
,
,
,

,,,

,,,

,,,

,,,

,,,

,,,
,
,
,
,
,
,

,,,

,,,

,,,
,
,
,

,,,

,,,

,,,
,
,
,

,,,

,,,

,,,
,
,
,
,,,
,
,
,

,
,
,

,,,
,
,
,,,

,
,
,

,,,
,
,


,
,
,,,
,,,
,
,


,
,
,,,
,
,
,

,
,
,
,,,
,,,
,
,


,
,
,
,,,
,,,
,
,


,
,
,,,
,,,
,
,


,
,
,,,
,
,
,

,
,
,
,,,
,,,
,
,


,
,
,

,,,
,
,
,,,

,
,

,,,
,
,


,
,
,,,
,
,
,

,
,
,

,,,
,
,
,,,

,
,

,,,
,
,
Logarithmi.
,
,
,

,,,
,
,


,
,
,,,
,,,
,
,

Num.
absolu.

,

,,,
,

250
Briggs’ 1624 table of logarithms (reconstruction, D. Roegel, 2010)
Chilias nonagesima secunda.
Num.
absolu.

Logarithmi.
,,,
Num.
absolu.

Logarithmi.
,,,
,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,
,
,
,
,
,
,

,,,

,,,

,,,

,,,

,,,

,,,
,
,
,
,
,
,

,,,

,,,

,,,
,
,
,

,,,

,,,

,,,
,
,
,

,,,

,,,

,,,
,
,
,
,,,
,
,
,

,
,
,

,,,
,
,
,,,

,
,
,

,,,
,
,


,
,
,,,
,,,
,
,


,
,
,,,
,
,
,

,
,
,
,,,
,,,
,
,


,
,
,
,,,
,,,
,
,


,
,
,,,
,,,
,
,


,
,
,,,
,
,
,

,
,
,
,,,
,,,
,
,


,
,
,

,,,
,
,
,,,

,
,

,,,
,
,


,
,
,,,
,
,
,

,
,
,

,,,
,
,
,,,

,
,

,,,
,
,
Logarithmi.
,
,
,

,,,
,
,


,
,
,,,
,,,
,
,

Num.
absolu.

,

,,,
,

251
Briggs’ 1624 table of logarithms (reconstruction, D. Roegel, 2010)
Chilias nonagesima secunda.
Num.
absolu.

Logarithmi.
,,,
Num.
absolu.

Logarithmi.
,,,
,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,
,
,
,
,
,
,

,,,

,,,

,,,

,,,

,,,

,,,
,
,
,
,
,
,

,,,

,,,

,,,
,
,
,

,,,

,,,

,,,
,
,
,

,,,

,,,

,,,
,
,
,
,,,
,
,
,

,
,
,

,,,
,
,
,,,

,
,
,

,,,
,
,


,
,
,,,
,,,
,
,


,
,
,,,
,
,
,

,
,
,
,,,
,,,
,
,


,
,
,
,,,
,,,
,
,


,
,
,,,
,,,
,
,


,
,
,,,
,
,
,

,
,
,
,,,
,,,
,
,


,
,
,

,,,
,
,
,,,

,
,

,,,
,
,


,
,
,,,
,
,
,

,
,
,

,,,
,
,
,,,

,
,

,,,
,
,
Logarithmi.
,
,
,

,,,
,
,


,
,
,,,
,,,
,
,

Num.
absolu.

,

,,,
,

252
Briggs’ 1624 table of logarithms (reconstruction, D. Roegel, 2010)
Chilias nonagesima secunda.
Num.
absolu.

Logarithmi.
,,,
Num.
absolu.

Logarithmi.
,,,
,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,
,
,
,
,
,
,

,,,

,,,

,,,

,,,

,,,

,,,
,
,
,
,
,
,

,,,

,,,

,,,
,
,
,

,,,

,,,

,,,
,
,
,

,,,

,,,

,,,
,
,
,
,,,
,
,
,

,
,
,

,,,
,
,
,,,

,
,
,

,,,
,
,


,
,
,,,
,,,
,
,


,
,
,,,
,
,
,

,
,
,
,,,
,,,
,
,


,
,
,
,,,
,,,
,
,


,
,
,,,
,,,
,
,


,
,
,,,
,
,
,

,
,
,
,,,
,,,
,
,


,
,
,

,,,
,
,
,,,

,
,

,,,
,
,


,
,
,,,
,
,
,

,
,
,

,,,
,
,
,,,

,
,

,,,
,
,
Logarithmi.
,
,
,

,,,
,
,


,
,
,,,
,,,
,
,

Num.
absolu.

,

,,,
,

253
Briggs’ 1624 table of logarithms (reconstruction, D. Roegel, 2010)
Chilias nonagesima secunda.
Num.
absolu.

Logarithmi.
,,,
Num.
absolu.

Logarithmi.
,,,
,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,
,
,
,
,
,
,

,,,

,,,

,,,

,,,

,,,

,,,
,
,
,
,
,
,

,,,

,,,

,,,
,
,
,

,,,

,,,

,,,
,
,
,

,,,

,,,

,,,
,
,
,
,,,
,
,
,

,
,
,

,,,
,
,
,,,

,
,
,

,,,
,
,


,
,
,,,
,,,
,
,


,
,
,,,
,
,
,

,
,
,
,,,
,,,
,
,


,
,
,
,,,
,,,
,
,


,
,
,,,
,,,
,
,


,
,
,,,
,
,
,

,
,
,
,,,
,,,
,
,


,
,
,

,,,
,
,
,,,

,
,

,,,
,
,


,
,
,,,
,
,
,

,
,
,

,,,
,
,
,,,

,
,

,,,
,
,
Logarithmi.
,
,
,

,,,
,
,


,
,
,,,
,,,
,
,

Num.
absolu.

,

,,,
,

254
Briggs’ 1624 table of logarithms (reconstruction, D. Roegel, 2010)
Chilias nonagesima tertia.
Num.
absolu.

Logarithmi.
,,,
Num.
absolu.

Logarithmi.
,,,
,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,
,
,
,
,
,
,

,,,

,,,

,,,

,,,

,,,

,,,
,
,
,
,
,
,

,,,

,,,

,,,
,
,
,

,,,

,,,

,,,
,
,
,

,,,

,,,

,,,
,
,
,
,,,
,
,
,

,
,
,

,,,
,
,
,,,

,
,
,

,,,
,
,


,
,
,,,
,,,
,
,


,
,
,,,
,
,
,

,
,
,
,,,
,,,
,
,


,
,
,
,,,
,,,
,
,


,
,
,,,
,,,
,
,


,
,
,,,
,
,
,

,
,
,
,,,
,,,
,
,


,
,
,

,,,
,
,
,,,

,
,

,,,
,
,


,
,
,,,
,
,
,

,
,
,

,,,
,
,
,,,

,
,

,,,
,
,
Logarithmi.
,
,
,

,,,
,
,


,
,
,,,
,,,
,
,

Num.
absolu.

,

,,,
,

255
Briggs’ 1624 table of logarithms (reconstruction, D. Roegel, 2010)
Chilias nonagesima tertia.
Num.
absolu.

Logarithmi.
,,,
Num.
absolu.

Logarithmi.
,,,
,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,
,
,
,
,
,
,

,,,

,,,

,,,

,,,

,,,

,,,
,
,
,
,
,
,

,,,

,,,

,,,
,
,
,

,,,

,,,

,,,
,
,
,

,,,

,,,

,,,
,
,
,
,,,
,
,
,

,
,
,

,,,
,
,
,,,

,
,
,

,,,
,
,


,
,
,,,
,,,
,
,


,
,
,,,
,
,
,

,
,
,
,,,
,,,
,
,


,
,
,
,,,
,,,
,
,


,
,
,,,
,,,
,
,


,
,
,,,
,
,
,

,
,
,
,,,
,,,
,
,


,
,
,

,,,
,
,
,,,

,
,

,,,
,
,


,
,
,,,
,
,
,

,
,
,

,,,
,
,
,,,

,
,

,,,
,
,
Logarithmi.
,
,
,

,,,
,
,


,
,
,,,
,,,
,
,

Num.
absolu.

,

,,,
,

256
Briggs’ 1624 table of logarithms (reconstruction, D. Roegel, 2010)
Chilias nonagesima tertia.
Num.
absolu.

Logarithmi.
,,,
Num.
absolu.

Logarithmi.
,,,
,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,
,
,
,
,
,
,

,,,

,,,

,,,

,,,

,,,

,,,
,
,
,
,
,
,

,,,

,,,

,,,
,
,
,

,,,

,,,

,,,
,
,
,

,,,

,,,

,,,
,
,
,
,,,
,
,
,

,
,
,

,,,
,
,
,,,

,
,
,

,,,
,
,


,
,
,,,
,,,
,
,


,
,
,,,
,
,
,

,
,
,
,,,
,,,
,
,


,
,
,
,,,
,,,
,
,


,
,
,,,
,,,
,
,


,
,
,,,
,
,
,

,
,
,
,,,
,,,
,
,


,
,
,

,,,
,
,
,,,

,
,

,,,
,
,


,
,
,,,
,
,
,

,
,
,

,,,
,
,
,,,

,
,

,,,
,
,
Logarithmi.
,
,
,

,,,
,
,


,
,
,,,
,,,
,
,

Num.
absolu.

,

,,,
,

257
Briggs’ 1624 table of logarithms (reconstruction, D. Roegel, 2010)
Chilias nonagesima tertia.
Num.
absolu.

Logarithmi.
,,,
Num.
absolu.

Logarithmi.
,,,
,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,
,
,
,
,
,
,

,,,

,,,

,,,

,,,

,,,

,,,
,
,
,
,
,
,

,,,

,,,

,,,
,
,
,

,,,

,,,

,,,
,
,
,

,,,

,,,

,,,
,
,
,
,,,
,
,
,

,
,
,

,,,
,
,
,,,

,
,
,

,,,
,
,


,
,
,,,
,,,
,
,


,
,
,,,
,
,
,

,
,
,
,,,
,,,
,
,


,
,
,
,,,
,,,
,
,


,
,
,,,
,,,
,
,


,
,
,,,
,
,
,

,
,
,
,,,
,,,
,
,


,
,
,

,,,
,
,
,,,

,
,

,,,
,
,


,
,
,,,
,
,
,

,
,
,

,,,
,
,
,,,

,
,

,,,
,
,
Logarithmi.
,
,
,

,,,
,
,


,
,
,,,
,,,
,
,

Num.
absolu.

,

,,,
,

258
Briggs’ 1624 table of logarithms (reconstruction, D. Roegel, 2010)
Chilias nonagesima tertia.
Num.
absolu.

Logarithmi.
,,,
Num.
absolu.

Logarithmi.
,,,
,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,
,
,
,
,
,
,

,,,

,,,

,,,

,,,

,,,

,,,
,
,
,
,
,
,

,,,

,,,

,,,
,
,
,

,,,

,,,

,,,
,
,
,

,,,

,,,

,,,
,
,
,
,,,
,
,
,

,
,
,

,,,
,
,
,,,

,
,
,

,,,
,
,


,
,
,,,
,,,
,
,


,
,
,,,
,
,
,

,
,
,
,,,
,,,
,
,


,
,
,
,,,
,,,
,
,


,
,
,,,
,,,
,
,


,
,
,,,
,
,
,

,
,
,
,,,
,,,
,
,


,
,
,

,,,
,
,
,,,

,
,

,,,
,
,


,
,
,,,
,
,
,

,
,
,

,,,
,
,
,,,

,
,

,,,
,
,
Logarithmi.
,
,
,

,,,
,
,


,
,
,,,
,,,
,
,

Num.
absolu.

,

,,,
,

259
Briggs’ 1624 table of logarithms (reconstruction, D. Roegel, 2010)
Chilias nonagesima tertia.
Num.
absolu.

Logarithmi.
,,,
Num.
absolu.

Logarithmi.
,,,
,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,
,
,
,
,
,
,

,,,

,,,

,,,

,,,

,,,

,,,
,
,
,
,
,
,

,,,

,,,

,,,
,
,
,

,,,

,,,

,,,
,
,
,

,,,

,,,

,,,
,
,
,
,,,
,
,
,

,
,
,

,,,
,
,
,,,

,
,
,

,,,
,
,


,
,
,,,
,,,
,
,


,
,
,,,
,
,
,

,
,
,
,,,
,,,
,
,


,
,
,
,,,
,,,
,
,


,
,
,,,
,,,
,
,


,
,
,,,
,
,
,

,
,
,
,,,
,,,
,
,


,
,
,

,,,
,
,
,,,

,
,

,,,
,
,


,
,
,,,
,
,
,

,
,
,

,,,
,
,
,,,

,
,

,,,
,
,
Logarithmi.
,
,
,

,,,
,
,


,
,
,,,
,,,
,
,

Num.
absolu.

,

,,,
,

260
Briggs’ 1624 table of logarithms (reconstruction, D. Roegel, 2010)
Chilias nonagesima tertia.
Num.
absolu.

Logarithmi.
,,,
Num.
absolu.

Logarithmi.
,,,
,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,
,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,

,,,
,
,
,
,
,
,

,,,

,,,

,,,

,,,

,,,

,,,
,
,
,
,
,
,

,,,

,,,

,,,
,
,
,

,,,

,,,

,,,
,
,
,

,,,

,,,

,,,
,
,
,
,,,
,
,
,

,
,
,

,,,
,
,
,,,

,
,
,

,,,
,
,


,
,
,,,
,,,
,
,


,
,
,,,
,
,
,

,
,
,
,,,
,,,
,
,


,
,
,
,,,
,,,
,
,


,
,
,,,
,,,
,
,


,
,
,,,
,
,
,

,
,
,
,,,
,,,
,
,


,
,
,