Addendum to MSS 399: American and Canadian Ciphering Books
SUMMARY OF CIPHERING BOOKS AT PHILLIPS LIBRARY, SALEM, MASSACHUSETTS
Nerida F. Ellerton and McKenzie A. Clements
Illinois State University, Department of Mathematics
During the period from May 26 to June 4, 2009, we had the opportunity to visit the Phillips Library (formerly, the Essex Institute
Library) in Salem Massachusetts, and with the generous assistance of the Library’s research section, were able to examine carefully the
extensive collection of ciphering/mathematics/navigation books within that Library. Our examination of the ciphering books held within the
Phillips Library, and within other leading historical collections in the United States, has left us in no doubt that the Phillips Library holds the
largest collection of eighteenth-century ciphering books held by any public institution or library in the United States. With the help and
encouragement of Sidney Berger (Ann C. Pingree Director of the Phillips Library), Irene Axelrod (Head Research Librarian), Andrew
French (Library Assistant), and Kathy Flynn (Head of Reference Services), all of whom work within the Peabody Essex Museum (of which
the Phillips Library is part), we compiled the following summary of ciphering books held by the Library. Further searching within the
Library archives would locate more ciphering books.
In our summary we have listed manuscripts in the chronological order in which they were written, except when there are several from
the one family – in those cases, different family members’ manuscripts have been listed successively as a group.
For the purposes of deciding whether a manuscript came within the ambit of the following list, we defined a ciphering book as a book
with the following three properties:
1. All entries in the book appeared as handwriting in ink, or as illustrations. Headings and sub-headings were presented in a
decorative, typically calligraphic style.
2. The book was dedicated to setting out rules and cases associated with mathematical topics, and included problems and exercises
linked to the topics. The problems were in arithmetic, especially business arithmetic, or in algebra, geometry, trigonometry, or
applications of mathematics in the fields of navigation, surveying, military strategy, etc
3. The content was sequenced so that it became progressively more difficult. The content also reflected the expectation that no child
less than 10 years of age was normally assigned the task of preparing a ciphering book.
Most of the ciphering books that we examined in the Phillips Library were concerned with either Arithmetic or with Navigation. Some of the
manuscripts had sections focusing on “Astronomy,” and one on “Dialling.” In the eighteenth and nineteenth centuries in North America,
ciphering books were usually comprised of unlined, rectangular folio-sized paper sheets (sometimes “rag” paper was used), and in most cases
dimensions were of the order of 12.5” by 8.” The pages were grouped as “quires,” and completed quires were routinely sewn together to
form books. Sometimes, protective covers were added. Typically, the first page of a ciphering book was beautifully decorated, and indicated
the name of the owner, as well as the year(s), and location in which the book was prepared.
Although the concept of “completeness” is not included in the above definition, ciphering books usually dealt with problems from a
number of topics. The treatment of any one topic occurred on successive pages. It was not usual for topics to be revisited at various times in
the same ciphering book, but occasionally this did happen. Ciphering books were intended to serve as reference books for future use by those
who prepared them.
©2009
Page 1A
Addendum to MSS 399: American and Canadian Ciphering Books
LIST OF CIPHERING BOOKS AT PHILLIPS LIBRARY, SALEM, MASSACHUSETTS, MAY–JUNE 2009
(As examined by N. F. Ellerton and M. A. Clements, with the Assistance of Library Staff)
Note that in the following the acronyms IRCEE and PCA are occasionally used to describe the genre of text. With IRCEE, the “I” denotes “Introductory comments”;
“R” denotes “Rules”; “C denotes “Cases”; the first “E” denotes a (model) example; and the second “E” denotes “Exercises.” With PCA, the first “P” denotes
“Problem”; the “C” denotes “Calculation”; and the “A” denotes “Answer.”
# of
m/s
Year(s)
Name
Gender
# of
Pages
Dimensions of
Pages
1
1727
DEXTER
Richard
2
17271728
3
M
36
GOODHUE,
Benjamin (Sr.)
M
44
12.5”
by
7.75”
14.75”
by
9.5”
1757
GOODHUE,
Stephen
M
84
12.5”
by
7.75”
and
12” by
7.25”
Elementary
Geometry,
Trigonometry,
Navigation
Straight edge/compass
constructions, various
kinds of sailing
Medium,
mature
4
1763
GOODHUE,
Jonathan
M
120
7.75”
by
6.25”
Geometry,
Surveying,
Dialling,
Trigonometry,
Navigation
Straight edge/compass
constructions, plain scale,
surveying. All the various
kinds of sailing are dealt
with.
Medium/
high
5
1784
M
84
M
Approx
360
4 operations, compound
operations, Rule of Three
Chronology, square and
cube roots, straight
edge/ruler constructions,
right angle and oblique
trigonometry, compass
variation, various forms of
Medium
17271728
12.5”
by 7.5”
12.75”
by
7.5”
Arithmetic
6
GOODHUE,
Benjamin (Jr.)
MOOR,
David
©2009
Mathematica
l Themes
Covered in
the M/s
Arithmetic
Elementary
Arithmetic
Geometry,
Trigonometry,
Navigation
Main Topics Covered
Numeration, four
operations, measures,
reduction, Rule of Three
Numeration, four
operations, compound
operations, measures,
reduction, Rule of Three
Quality,
Penmanship,Calligraphy
Medium
Low/
medium
High
Comments
Lots of hogsheads, etc. Mark = 13/4, Noble
= 6/8. Note on longitude.
A 3 by 3 magic square is shown. E.g.,
“There is a stand of 5 foot 9 inches long, 4
foot 7 inches broad, and 2 foot 8 inches
deep. I demand how much foot [sic] there
is contained in the stand. “To obtain the
answer, 69 by 55 by 32 was calculated, and
the product was then divided by 1728.
There is a plan of an “intended” journey
from Salem to the West Indies. Wording of
questions relating to the “Julian Kalendar”
is identical to wording in Ebeneezer
Bowditch’s 1747-1751 m/s (It is possible
that they used the same textbook). Rough
cloth covers.
Medium/high, with several well-drawn
diagrams in ink, and an attractive mariner’s
compass on the inside back covers. There is
a reference to John Winthrop’s A Table of
Variation of Compass. There is no journal
for a trip.
Rough decorative cover, sewn on. See also
Goodhue, 1727-8
There is a beautiful, multi-colored compass
drawn, and there are also creative,
“dynamic: diagrams (with moving parts).
This m/s has a strong Christ’s Hospital feel
about it. “David Moor – His Book
Navigation, Details of an Intended Trip
Page 2A
Addendum to MSS 399: American and Canadian Ciphering Books
7
17311734
ADAMS,
Jedediah
M
46
7.25”
by 6”
Geometry
8
17371744
LUCKIS,
Benjamin
M
124
12.5”
by
8”
Geometry,
Trigonometry,
Navigation
9
1740
Unidentified
M
72
12.5”
by
8”
Geometry,
Trigonometry,
Navigation
10
circa
1740
ANNABLE,
Ephraim
M
103
12” by
7.5”
11
17491751
BOWDITCH,
Ebeneezer
(died 1771)
M
100
12.5”
by
7.5”
Geometry,
Measurement
of
Superficies,
Trigonometry,
Navigation,
Gauging
Elementary
Geometry,
Trigonometry,
Navigation
Arithmetic
©2009
sailing (plane, oblique
traverse, middle latitude,
Mercator, globical [sic]),
journal keeping,
astronomy, gauging
Straight edge/ compass
constructions, definitions
of polygons (and
associated problems. There
is a lengthy section on
dialling.
The Julian Calendar,
straight edge/compass
constructions,
trigonometry, various
kinds of sailing (plane,
traverse, middle latitude,
Mercator, parallel),
variations of a compass,
journal keeping on
voyages.
Straight edge/ compass
constructions, definitions
of polygons (and
associated problems, types
of sailing)
Straight edge/ compass
constructions, definitions
of polygons (and
associated problems, types
of sailing, heights and
distances
Straight edge/ compass
constructions, various
kinds of sailing (a very
colorful mariner’s compass
(water-colored) Log of a
journey from Salem to
Charlestown (South
Carolina)
from Lizard to Barbados. Begun Feb 1st,
1727.”
Low/
medium
Medium/
high
This in an unlined book, with battered
“marbled” covers (which were probably
added “later”). The theme is practical
geometry. The level of penmanship and
calligraphy is low/medium. IRCEE genre is
evident throughout.
Facing the last page, one finds: “Rules for
correcting your dead reckoning by an
observation of the sun or stars.” Badly
stained, ornate wording, marbled covers.
Low/
medium
Many words are misspelled (e.g., “angel,”
“paralall.” IRCEE genre evident
throughout, but not PCA (answers are often
stated in sentences).
Low/
medium
IRCEE and PCS genres evident throughout.
A trapezium is defined as an irregular
quadrilateral.
Medium,
mature
At the end of the book there is a log of an
apparently real voyage from Salem aboard
the schooner Tyrall (voyage started July 12,
1751). Wording of questions relating to the
“Julian Kalendar” is identical to wording in
Ebeneezer Bowditch’s 1747-1751 m/s (It is
possible that they used the same textbook).
Hard (marbled) cover, with “leather” spine
cover.
Page 3A
Addendum to MSS 399: American and Canadian Ciphering Books
12
1750
BOWDITCH,
John
M
46
13
circa
1800
Possibly
attributed to
BOWDITCH,
Nathaniel
M
37
14
1755
RAFFLES,
Benjamin
(Coldham
(1990) states
that Raffles was
baptized July
29, 1739, and
was son of
Thomas R.
Raffles.)
M
12.5”
by
7.5”
14.75”
by
9.25”
740
11.5”
by
8.75”
.
15
1756
WALTERS,
William
M
48
12” by
7.5”
16
1758
PLUMER,
Asa
(1742-1800)
(Prepared in
Rowley, MA)
M
18
7.75”
by
6.25”
©2009
Navigation
Elementary
axiomatic
geometry, to
diagrams for
mensuration
of heights and
distances
Standard
Christ’s
Hospital RMS
curriculum.
See (Coldham,
P. W. (1990).
Child
apprentices in
America from
Christ’s
Hospital,
London, 16171778.
Baltimore,
MD:
Genealogical
Publishing Co
Arithmetic,
Trigonometry,
Surveying,
Navigation
Arithmetic
Various kinds of sailing.
Assumes knowledge of
trigonometry.
Geometry, navigation,
astronomy
Medium,
mature
“Lattitude” (sic) is repeatedly spelt
incorrectly, throughout the m/s. No covers.
High/
magnificent
Included are some incredible diagrams on,
for example, “projection of solar eclipse of
Portland.” It is conjectured that this was
Nathaniel Bowditch’s work. Pagination: 131 and 66-87; missing 32-65; 28 bound
pages, plus loose page on Trigonometry, 1
loose page on spheres, and 7 loose pages on
solar eclipse, which include illustrations.
All the standard Christ’s
High. This
The leather-bound m/s has Sir T. Stamford
Hospital RMS curriculum m/s features Ruffles ownership form on the inside front
topics (and features) are
beautiful
cover. There are the gilt royal
present except there is no
pen/ink
insignias/seals on the front and rear covers.
log of an actual, or even an drawings
Benjamin was admitted to Christ’s Hospital
intended, journey.
(especially
from St Ann Blackfriars, and on July 12,
on page
1755, was apprenticed to Mr. George
310).
Hooper, of the Martin, bound for Antigua.
It is intriguing that Raffles’ m/s is dated
1755, and does have a log of an actual or
intended journey. This m/s originated from
the Royal Mathematical School (RMS) in
Christ’s Hospital, London, and not in
America.
Trigonometric ratios, plain,
traverse, Mercator’s and
middle latitude sailing,
square, cube and sursolid
roots
Low/
medium
Subtraction, multiplication
division, addition of
money, troy weight
Low
IRCEE genre evident throughout. Tables
were prepared for the log of a journey, but
these were not completed. A knowledge of
logarithms, and of Gunter’s scale, was
assumed. Marbled covers, leather spine
cover; front cover is torn.
The name Thomas Plumer (1762) also
appears on the m/s, but seems to have been
a later addition. Almost everything is
calculation – but there are a few short
descriptions. E.g., “Substraction teacheth to
take a small sum from a great one that the
difference may be known,” “Beauty soon
fades” Hand sewn, between thick covers.
Page 4A
Addendum to MSS 399: American and Canadian Ciphering Books
17
1763
ORNE,
Timothy Jr.
M
64
12.5”
by
7.75”
Arithmetic
18
17631764
KNIGHT,
Edmund
M
74
12” by
7.75”
19
17701774
KNIGHT,
Joseph
M
32
13” by
8.25”
Arithmetic,
some
Geometry,
Trigonometry,
and
Navigation
Arithmetic
20
1767
JANEWAY,
James
(Janeway is
not listed in
Coldham text
(1990)
M
Approx
650
11.5”
by
9”
Standard
Christ’s
Hospital RMS
curriculum
This standard Christ’s
Hospital RMS ciphering
book includes the usual
comprehensive curriculum
topics (and features) and
the log of what seems to
have been an actual,
journey from “England
towards Madeira).”
High
21
1767
LITTLE,
Josiah
M
88
12.75”
by
7.75”
Arithmetic,
Geometry,
Trigonometry
Medium/
high
22
1773
MORGAN.
Jacob Gray
M
92
12” by
7.5”
Elementary
Geometry,
Navigation
Decimals, Standard
elementary geometry
constructions, various
types of sailing,
mensuration, gauging,
surveying
Geometrical problems,
different kinds of sailing,
log of a journey to
Bordeaux in 1773
23
1774
TIFFIN,
Henry
(1748-1776)
M
360
©2009
Navigation
Numeration, 4 ops,
measures, Rules of 3,
Practice, Interest (S & C),
Fellowship.
Decimals, Exchange,
interest, measures, Rule of
Three, Fellowship (with &
w/out time), Plane
geometry, trigonometry,
plane and traverse sailing
4 ops, reduction, Rules of
Three, Practice, Fellowship
Straight-edge compass
constructions,
trigonometry, profiles of
coastlines, various kinds of
Medium/
High
From a prominent Salem family. All
“proofs” are shown.
Low
Very practical, calculations everywhere.
First page is all about hogsheads, gallons,
etc. Note that he had 50 lessons with Master
Moody, 45 on arithmetic, 5 on geometry.
Total cost was 2/14/6. See also Joseph
Knight, 1770-1774.
With the m/s are 4 pages (pp. 134-7) from
the Youth’s Instructor in the English
Tongue, by John Owens (1732). Theirs was
known as the New England Spelling Book.
See also Edmund Knight, 1763-1764
There is a gilt royal insignia/seal on the rear
cover. Unlike the Benjamin Raffles Christ’s
(1755) Hospital m/s this one does have a
log of an actual journey. “Martin
Gillingwater 1772” and “John S. Bassett
1859” are on the front cover (in addition to
James Janeway 1767). This m/s originated
from the Royal Mathematical School
(RMS) in Christ’s Hospital, London, and
not in America. As would befit a Christ’s
Hospital m/s, there are beautiful pen/ink
drawings. Drawings, some with water
color. The front leather cover is missing.
The soft cover has a “marbled” effect but
the date was clearly indicated on the inside
front cover. Medium penmanship and
calligraphy, with neat ink line diagrams.
All in one quire.
Low/
Medium
Medium
Breathtaking/
stunning!
In 1783, the book was bought by Wesley
Burnham from Jacob Gray Morgan (born
1747). Burnham would subsequently
become a Captain. Marbled (thin cover)
card covers.
This is simply a magnificent m/s, with
superb water-colored art work. The m/s
appears to have been a book that Henry
kept to pass the time on board when he was
Page 5A
Addendum to MSS 399: American and Canadian Ciphering Books
Prepared on
board ships
(e.g., Eagle,
Panther,
sailing (plain, oblique,
Mercator, middle latitude.
Logarithms
24
1776
HASKELL,
Isaac (Junior)
M
154
13” by
8.25”
Measurement,
Surveying,
Gauging,
Navigation,
Astronomy
25
17771778
CURRIER,
John
M
120
12.5”
by
8”
26
Circa
1780s
NICHOLLS,
Ichabod
M
120
13” by
8”
Elementary
Geometry
Navigation
Log of a
Journey
Arithmetic
27
1781
TOWNSHEND,
Samuel
M
156
28
17831785
PEELE,
Robert
M
32
©2009
Arithmetic
12” by
7.25”
Arithmetic
Various measures,
gauging, various forms of
sailing, including a section
on great circle sailing
an apprentice navigator in 1774. Some of
the paintings seem to have been copied
from other works. Some of the paintings are
dated 1758 and 1759 (when Henry was
aged 10-11). (Some of the paintings are
dated 1758 and 1759. Full leather covers,
repaired and bound. Prepared on board
ships (e.g., Eagle, Panther)
Low
Straight edge/ ruler
constructions, various
forms of sailing, planned
voyages
Rule of Three, practice,
interest (S & C), annuities,
fellowship (with & w/out
time), Barter, equation of
payments, rebate or
discount, exchange,
alligation (M & A), single
& double P, vulgar
fractions, decimals.
Measures, tare and tret,
simple interest
Medium/
High
Fellowship, barter,
equation of payments,
discount, exchange, loss
and gain
Medium/
high
Note: This ciphering book can be found in
Phillips Library MSS 322, Henry Tiffin
The m/s is sewn between heavy hessian
covers. IRCEE genre is evident throughout.
Benjamin Harrick and Eunice Haskell were
married on November 25, 1747, but were
lost at sea. The next year, Lucy was born on
August 18, 1748.
The planned journey was from England to
Barbados, in October 1777. Then, there was
an intended journey from England towards
Madeira in 1778. The influence of Christ’s
Hospital is writ large.
Pages were mostly arranged in signatures of
28. Red ink was used for emphasis. Loose
pages, in old card cover.
Front page: “Robert Peele, his book and
pen, God bless George Washington and all
his men” (The year was 1783!)
Page 6A
Addendum to MSS 399: American and Canadian Ciphering Books
29
1784
Unidentified
30
1785
31
circa
1805
32
1785
FELT,
Joseph
(Senior)
FELT,
Joseph
(attended
North School,
Salem)
HERRICK,
Peter
33
1787
SILVER
William
34
circa
1788
Unidentified
35
17901791
LANDER,
William
©2009
64
12.75”
by
8”
M
88
M
46
12.5”
by
7.5”
12.5”
by
8”
M
90
M
160
M
Elementary
Geometry,
Trigonometry,
Navigation,
Log of a
Journey
Arithmetic
Straight edge/ ruler
constructions, trigonometry
various forms of sailing,
planned voyages
IRCEE genre evident, with many cases.
There was much “prepperation” and
“mecator” and “lattitude” were studied.
There was a log of an intended voyage from
Salem to Barbados aboard the brig
“Charming.” No covers.
Many practical examples. IRCEE genre
evident.
Reduction, measures, Rule
of three, fellowship, barter
Medium/
high
Arithmetic
Measures, compound
operations, Federal money,
reduction
Medium
The book (in which the m/s was presented)
was sold by Samuel West, in Essex Street,
Salem. Marbled covers, card.
13” by
8”
Arithmetic
Medium/
high
M/s was passed on to Robert Barr who
wrote: “Excuse my writing, for I had no
ruler nor (sic) plummet.” Oversized, thick
cover.
11.75”
by 8”
Arithmetic,
Geometry,
Trigonometry,
Navigation
Numeration, practice,
rebate, fellowship, barter,
equation of payments, loss
or gain, exchange,
allegation (M & A), Rule
of Three (single and
double)
Gregorian callandar [sic], 4
operations, reduction, Rule
of Three, (sic.), Straight
edge /compass
constructions, plane
sailing, trans-verse sailing,
middle-latitude sailing,
Mercator’s sailing
Measures, Rule of Three (S
& D), practice
Middle
“Plan of a voiyage [sic] towards Barbadoes
[sic]– it is possible it actually happened –
from Cape Cod. Perhaps, though the real
journey was from Salem to Cadiz (for this
is said to have happened in June 1787).
32
12” by
7.5”
Arithmetic
312
7.5” by
6”
Arithmetic,
Trigonometry
Elementary
Geometry,
Trigonometry
Numeration, 4 operations,
compound operations,
measures, vulgar fractions,
decimals, Federal money,
rule of three, compound
proportion, fellowship,
practice, tare and tret,
involution, evolution,
arithmetical progressions,
alligation (alternate), single
Medium
Medium/
high
IRCEE, but not PCA genre evident
throughout.
“If 6 ells of ___ cost 18/-, what will 48 ells
cost?” Response was to multiply 18 by 48
and then to divide by 6 and by 20.
The teacher often did the headings, and
wrote the problems in the book. There us a
letter in the ciphering book (from a
descendant) in which that is pointed out,
and certainly careful examination of the
manuscript reveals quite different writing
styles. Marbled covers.
Page 7A
Addendum to MSS 399: American and Canadian Ciphering Books
36
1791
37
1791
WAITTS,
Aaron
SHORT,
Peter
M
42
M
92
13” by
8”
11.75”
by
7.25”
Arithmetic
Geometry,
Trigonometry,
Navigation.
At the end of
the book there
is a log of an
actual journey
from Boston
towards
Halifax, and
another from
London
towards
Madeira.
38
1792
Unidentified
39
1793
CLEVELAND
George
40
1793
MANNING,
Mary
©2009
48
12” by
7.25”
Navigation
M
96
12.25”
by
7.25”
Arithmetic
F
15
12.75”
by
7.75”
Elementary
Arithmetic
and double position,
permutations, and
combinations, elementary
geometry, trigonometry
Compound operations,
measures, Rule of Three.
Straight edge/compass
constructions, definitions
of polygons (and
associated problems)
Medium/
high
Medium
.
There is a lengthy section
on dialling.
Plane sailing, traverse
sailing, middle-latitude
sailing, Mercator’s sailing
Various kinds of Sailing
(mecator, [sic], middle
latitude, etc.),
Log of Intended Journey
Interest (S & C), annuities,
fellowship (with & w/out
time), Rules of Three (D &
I), inverse proportion,
practice, barter, equation of
payments, rebate or
discount, exchange,
alligation (M & A), single
& double P, vulgar
fractions, decimals, loss
and gain, brokerage,
commission.
Numeration, four
operations
Medium
Hogsheads, molasses, etc. – all very
relevant to Salem.
The book has a soft “marbled” cover. It is
not clear if this was added later. On the
inside of the front cover is an advertisement
by Osgood Carleton, of Boston, indicating
that Navigation classes are offered. “Books,
quadrants, sea charts, scales, etc., procured
for pupils at the cheapest rate. In teaching
navigation the most approved rules for
correcting the dead reckoning by sea by
observation are attended to. The use of
charts and Gunter’s scale, &c, is also
taught.” Also taught were “plans or maps of
surveys, either from the minutes taken by
the surveyor, or from other maps.” Osgood
Carleton claimed to teach surveying,
gauging, mensuration, algebra, geometry,
geography, astronomy, dialling, gunnery,
architecture.
The intended (and perhaps actual) journey
was from Salem to the Cape of Good Hope.
This may have taken place in 1792.
Medium/
high
The order of treatment of topics was not
strictly logical.
Medium
Mary used strong, large handwriting. She
married Captain Thomas Bedford.
Page 8A
Addendum to MSS 399: American and Canadian Ciphering Books
41
17931794
OLIVER,
William W.
M
108
13” by
8”
Arithmetic
42
1794
WALDO,
Elle
F
156
7.25”
by 6”
Arithmetic,
Geometry,
Trigonometry,
Navigation
43
1798
WALDO,
Charles F.
M
110
13” by
8”
Geometry,
Trigonometry
and
Navigation
(Full
leather
covers)
44
1796
COLE,
Thomas
M
120
9.25”
by 7”
Geometry,
Trigonometry,
Navigation,
Surveying
45
circa
1799
BURNHAM,
Elizabeth D.
F
72
13” by
8”
Arithmetic
©2009
Measures, tare and tret,
reduction, Rule of Three,
practice, simple and
compound interest
Medium
Loss and gain, equation of
payment, commission,
brokerage, policies &
insurance, practice, tare &
tret, involution, vulgar
fractions, progressions (A
& G), alligation (M & A),
S & D position,
straightedge, compass
const-ructions,
trigonometry, plain and
traverse sailing
Straight-edge and compass
constructions,
trigonometry, sailing
Medium/
high
Elementary axiomatic
geometry (after Euclid),
plane scales, conic
sections, projections of
sphere
Numeration, four operaions, compound operations,
reductions, decimals, Rule
of Three
High/
magnificent
High
(welldrawn ink
illustrations)
Medium
“If you borrow, return.”
“Bought 19 chaldrons of coats at 29/6 per
chaldron. What came they to?”
Written on a gravestone:
“Behold and see as you pass by
As you are now so once was I.
As I am now, so you must be
Prepare for death and follow me.” (William
Oliver, 1793)
Includes C. Waldo, 1799; Plane Sailing,
Traverse Sailing (on reverse side, back of
book)
Penmanship and calligraphy are at a high
level, with neat ink illustrations. IRCEE
genre evident throughout. There are logs for
two journeys at the end of the book – the
first was the model London to Madeira
(begun April 1, 1795, on the Frances of
London, under by William Johnson, and the
second, real journey from Salem to Cardiz,
on board the Astrea, begun August 25,
1798.Entries in the first journey are
copperplate, but those for the second, real
journey are much less neat!
Amazing water-color illustrations in a
section on “mensuration of heights and
distances.” Excellent penmanship, superb
calligraphy.
Sewn between soft, grey covers
Page 9A
Addendum to MSS 399: American and Canadian Ciphering Books
46
1828
BURNHAM,
Rebecca
F
32
7,75”
by
6.25”
Elementary
Arithmetic
47
1800
BENT,
Rose
F
84
12” by
7.25”
Arithmetic
48
circa
1800
DEVEREUX,
James
M
96
49
circa
1800
DONES,
Ellen A Stowe
(?)
F
32
9.5” by
7.5”
Arithmetic
50
circa
1800
TRESON,
John
M
40
7.5” by
6”
Arithmetic
51
1804
INGERSOLL,
John (Senior)
M
210
©2009
Arithmetic
106
Elementary
pages are
Geometry,
12’ by Trigonometry,
7.5”,
Navigation,
28 pages
Surveying
are 12”
by 7.5”,
76 pages
are 11.5”
by 7.25”
Numeration, four operations. Compound operations, measures, single
Rule of Three
Commission and
brokerage, insurance,
discount, banking, equation
of payments, barter, loss
and gain, allegation (M &
A), S & D position,
exchange
Compound operations,
reduction (ascending and
descending), Rule of Three
(S & D), fellowship, barter
Measures, 4 operations,
compound operations,
reduction, Rule of Three
direct
Straight-edge/compass
constructions, right-angled
and oblique trigonometry,
elementary surveying
(plotting a field), variation
of the compass, projection
of plane scales, various
kinds of sailing, log of
journal of voyage
Medium/
high
This m/s was handwritten within had
commercially-produced covers.
Medium/
high
“The capture of Gen Burguoyne and his
army happened in the year 1777; that of
Cornwallis in 1781. How many years
between these events?” Answer given
showed 1781–1777, giving 0004, and this
answer was proved by adding.
Medium
Red ink was used to divide some of the
pages into columns.
Medium
There is a lengthy section on division.
“John Treson, his book” appears
throughout.
Medium/
High
IRCEE genre is evident throughout. This
follows the standard elementary navigation
curriculum, together with some elementary
geometry and surveying. When the log for
the journal in this book was compared with
that for Ephraim Emmerton Jr., it was
found that entries were identical, except
that one Emmerton’s journey began on
March 25, 1808, and this on March 25,
1801. (“At noon, got underway with a fine
breeze from the NW …”)
There are
some
attractive
line
drawings
in ink.
Page 10A
Addendum to MSS 399: American and Canadian Ciphering Books
52
53
circa
1840
18021808
INGERSOLL,
John G.
(Junior)
WOODBERRY,
Isaac K.
M
M
48
108
13” by
8”
13” by
8”
Arithmetic
(elementary to
advanced)
Arithmetic,
Geometry
High.
Numeration through to
single and double
Beautiful
position, APs, GPs
penmanship.
(progressions),
permutations, involution,
duodecimals, promiscuous
questions
Medium/
Notation, numeration, 4
high
operations, compound
operations. Measures, rule
of Three (D & I), vulgar
fractions, fellowship (S &
D), tare and tret,
involution, interest (S &
C), barter, discount, loss
and gain, equation of
payments, alligation
(medial and traverse),
single position,
geometrical problems
Various types of sailing,
High
projections of the sphere,
log of a journey –
probably not a real one
54
1803
ABERRINZER,
Lowell
M
Approx
400
12.5”
by
7.5”
Navigation,
Geography
55
18031806
WAIT,
Harriet
F
37
13” by
8”
Arithmetic
Rule of Three (D &
inverse), interest (S & C),
interest, exchange, profit
and loss, barter,
miscellaneous
Medium
(small &
neat)
56
circa
1805
Unidentified
110
12.5’ by
7.5”
Arithmetic
Compound operations,
measures, decimals, Rule
of Three, vulgar fractions,
tare and tret, then
fellowship, simple
interest, compound
interest, commission and
Medium
©2009
Standard IRCEE and PCA genres are
evident throughout.
The m/s is sewn between soft “marbled”
commercially-produced covers.
Large signatures, sewn together between
soft covers. Last 10 pages were added later.
These are based on a 2-page drawing of the
polar system “orbit of Saturn,” done March
24, 1808.
Some topics were repeated, with different
setting out, later in the m/s. Elementary
straight edge and compass constructions
were included at the end of the m/s.
There are some beautiful ink drawings (e.g.,
a mariner’s compass in color). Included is a
log of a “journey” from Boston to Madeira
(began in March, 1801). A strong Christ’s
Hospital influence seems to be apparent.
This m/s is between commercially-prepared,
soft covers. On the inside front cover there
are “Necessary Tables in Arithmetic” by
John Southwick, schoolmaster in Salem.”
On the inside of the rear cover is printed
“More measures – time apothecaries’
weight, troy, weight, land measure, cubic or
solid measure, motion, Federal money,
reduction, tare and tret, the Rule of Three,
practice – printed by T. C. Cushing, Salem.”
The m/s is sewn with a large cardboard
cover, edged with khaki tape
Page 11A
Addendum to MSS 399: American and Canadian Ciphering Books
57
circa
1805
GARDNER,
George
M
68
12.5”
by
7.75”
Arithmetic
58
circa
1805
TOWNE,
Daniel
M
32
12” by
7.75”
Arithmetic
59
1807
CHEVER,
David
(born 1793)
M
48
7.75”
by
6.25”
Geometry,
Trigonometry
and Navigation
60
1808
BROOKS
William N.
(1793-1888)
M
160
7.75”
by
6.25”
Arithmetic
61
1808
DIMOND,
Benjamin
M
36
and 7
11.75”
by 7.2”
and 13”
by 8”
Arithmetic
©2009
brokerage, insurance,
general average, discount,
buying and selling stocks,
equation of payments,
barter, loss and gain,
alligation (medial &
alternate), position (S &
D), progressions,
permutations, square
roots, cube root,
duodecimals
Exchange, progressions
(AP & GP), permutations,
involution and evolution,
duodecimals.
Compound operations,
proportion, Rule of Three
(D & I), practice
Straight-edge and
compass constructions,
logarithms, projection of
plane scales,
trigonometry, Rule of
Three by logarithms,
navigation (e.g., plane
sailing)
Inverse proportion,
compound proportion,
tare & tret, weights &
measures, decimals,
duodecimals, APs,
cube/square/biquadratic
roots, exchange,
fellowship (S & D),
position (S & D), loss &
gain
Decimals, reduction,
Gregorian calendar
Medium/
high
Huge amount on currency exchange (perhaps
from Nicolas Pike).
Medium
IRCEE and PCA genres throughout.
Medium
(some welldrawn ink
illustrations
)
Penmanship and calligraphy are at a
medium level. Blank pages were sewn
together (by the commercial book seller,
Charles Steele (opposite Dr Holyoke’s), and
a “marbled” cover has been added
(probably at some later date).
Medium/
high
The commercially printed book was made
and sold by “Charles Steele, Essex Street
Salem, opposite Dr Holyoke’s.” Brooks
wrote at the front of this m/s, on January 1,
1888, that he now loved in Roxbury, MA
and he was now aged 94 years.
Medium
IRCEE genre evident throughout. Heavy
One of the manuscripts is sewn between a
heavy hessian cover with hem.
Page 12A
Addendum to MSS 399: American and Canadian Ciphering Books
62
1809
DIMOND,
Benjamin
M
50
11.75”
by
7.25”
Arithmetic
63
1809
BECKFORD,
Daniel
M
90
Elementary
Arithmetic
64
1809
PEELE,
Josiah B.
M
120
Various
(mainly
13” by
8”,
12.5”
by 8”)
12” by
7.25”
65
circa
1810
GAY,
Nancy D.
F
144
Arithmetic
66
circa
1810
Member of the
TOWNSEND
Family
F
48
9.25”
by
7.25”
10” by
7.75”
67
1810
Unidentified
11.5”
by
9.25”
Dialling
20
Arithmetic
Arithmetic
(In his later
years, Thomas
Jefferson
practiced
dialing as a
mental
exercise)
68
1810
ASPINWALL,
Samuel
M
70
12” by
7.5”
Elementary
Arithmetic
69
1811
COLBEY,
Benjamin
(who claimed
to be Chief
Mate of
M
120
12” by
7.5”
Navigation
©2009
Compound operations.
Weights and measures,
bills of parcels, compound
division. Decimals.
Numeration, four
operations, measures,
reduction
Numeration, practice,
rebate, fellowship,
measures, Rule of Three,
inverse and compound
proportion
Numeration, Rules of
Three (D & I), practice,
arithmetical progressions.
Numeration though to
Rule of Three direct,
exchange (between
federal and state
currencies)
Dialling. [This is the only
m/s found thus far in
which the focus is
exclusively on dialing.
There are many
definitions, cases, rules,
problems, but no
numbers.]
Four operations.
measures, compound
arithmetic, reduction,
practice, Rule of Three.
Various kinds of sailing,
and logs of two journeys.
This probably does not lie
within the category
“ciphering book”
Low/
medium
Medium
Most of the m/s comprises solutions to
problems, although occasionally IRCEE
genre is followed. The PCA genre is evident
throughout.
Topics were repeated (cloth measure, liquid
measure – similar questions, with different
quantities. “In 181918244 yards, how many
ells Flemish?” Hand sewn into old marbled
cover.
Medium/
bold
Presented to Essex Institute by American
Antiquarian Society, in 1945.
Medium/
high
Features hard covers, with leather spine
cover
High
Magnificent penmanship, calligraphy.
Interesting on need for metrication. Excellent
for need to adopt metric system if elementary
arithmetic.)
Medium
The word dialling originally referred to the
creation of the mathematics required to
create a sundial face to tell time based on
the position of the sun. Those skilled in the
art were referred to as diallists or
gnomonists; taken from the word “gnomon”
(a device using a shadow as an indicator).
The mathematician William Oughtred
published a book, Easy Method of
Mathematical Dialling, around 1600.
Samuel Aspinwall was “from Boston.”
Marbled covers.
Medium
Medium
This was a log of a journal from Cape Ann
to Martenico in the ship Industry, Joseph
Mills Commander, starting Feb 12, 1810.
There is also a plan for a journey from
Gloucester to London on the Ruby of
Page 13A
Addendum to MSS 399: American and Canadian Ciphering Books
70
1812
(Commenced
on Nov
9, 1812)
71
1812
72
Commander
Joseph Mills)
EMMERTON,
Ephraim
(Junior)
Gloucester, beginning Feb 16, 1810.
M
30
13” by
8”
Navigation
PARSONS,
Jeffrey
M
200
13” by
8”
Mercantile
Arithmetic
1814
BECKFORD,
Thomas
(Junior)
M
86
12.5”
by 8”
Arithmetic
73
1814
KNIGHT,
Eliza
F
70
12” by
7.5”
Elementary
Arithmetic
74
18161830,
1841
STIMPSON,
Thomas
M
About 7.5” by
400
6.75”.
pages
9.5” by
in total. 7.75”.
11.75”
by 7.25;
the
largest
volume
(with
134
pages)
is 12”
by
7.25.”
©2009
Advanced
arithmetic,
geometrical
calculations.
The 1841 m/s
is concerned
with middlelevel algebra.
Log of an “imagined”
voyage: Boston to
Madeira, Friday, March
25, 1808, to April 11,
1808. [c.f., log in journal
of John Ingersoll Senior,
1801.]
Measures, four
operations, etc.
Four operations,
Medium
measures, compound
operations, reduction,
decimals, single and
double Rules of Three
Numeration, 4 operations, Medium
measures, compound
arithmetic, Federal
money, decimals
Medium
Elementary topics
covered: division,
decimals, vulgar fractions,
Federal money, interest (S
& C), Rule of Three (S,
D), practice, involution
and evolution, duodecimals, loss and gain,
assessing taxes. General
rule for extracting the root
of all powers, general rule
for roots, progressions,
(AP, GPs), annuities,
alligation. Elementary
geometry included in one
volume, mechanics in
another. The algebra m/s
starts with “Section 5,
equations of the first
degree, then with sections
6, 7 and 8. Ch 9 deals
with generalization, Ch 10
As in some other journals, there is a
reference to “pleasant gales and fair
weather.” He also made an entry at the Bay
of Bengal, Sept 30, 1824, suggesting that he
was using his journal (prepared many years
before) as a model.
Solutions to some of the exercises were
entered more than once in the m/s (at
different places).
This m/s was between marbled card covers,
and had lined pages. 12 blank pages
included in page count.
IRCEE, PCA genres evident throughout.
IRCEE, PCA genres evident throughout.
There are 7 m/s, with 45, 48, 48, and 134
pages. The m/s on algebra has 34 pages, and
the volume on mechanics (with some
elementary algebra from Bailey’s Algebra)
has 58 pages (and mentions National
Arithmetic (probably Greenleaf).
Page 14A
Addendum to MSS 399: American and Canadian Ciphering Books
75
1819
DAVIS,
Solomon G.
76
circa
1820
Unidentified
77
circa
1820
Unidentified
78
79
©2009
1820
1820
Unidentified
DUNAMP,
James
M
M
M
148
12.25”
by
7.25”
Elementary
Geometry,
Trigonometry
Navigation
40
12.75”
by
7.75”
Arithmetic
12.5”
by
8”
(lined
paper)
Elementary
Geometry,
Astronomy
(uses
logarithms
throughout)
13” by
8.25”
Geometry,
Navigation
70
68
9.75”
by 8”
Arithmetic
with Evolution, and Ch 12
with miscellaneous
questions
Straight edge/compass
constructions, trigonometry, various types of
sailing, Gunter scale,
variations of the compass.
Logarithms are used
throughout
Rule of Three, inverse
proportion, compound
proportion, vulgar
fractions.
Straight-edge & Compass
constructions. Calculating
distances, traverse sailing,
parallel sailing, middle
latitude sailing,
Mercator’s sailing. Log of
a journey – probably
hypothetical – from
Boston to Madeira. Lunar
observations
Straight-edge & Compass
constructions. Calculating
distances, traverse sailing,
parallel sailing, middle
latitude sailing,
Mercator’s sailing.
Currency exchange,
progressions (A & G),
involution and evolution,
duodecimals
Middle
There are two handwritten inscriptions
indicating that this was being written in
Bombay in 1819. Inside the front cover is
written: “The lesson book of Captain
Solomon Davis,” Gloucester, MA.
Medium
There are no covers, and the front page is
detached. Standard of penmanship and
calligraphy is moderate. IRCEE and PCA
genres evident throughout. There is a
lengthy log of a journal from Boston to
Madeira – it seems as if it was an actual
journey. Each day there were standard
entries, and calculations are shown at the
bottom of the pages. Sewn as one signature.
The trip from Boston to Madeira was dated
Saturday March 25, 1820 to April 10, 1820.
“All this day fine breezes with very clear
weather.” Sewn between covers on which
governour’s [sic] speech is printed.
Medium/
high
Trigonometric knowledge is assumed from
the beginning.
IRCEE genre evident throughout.
Medium
IRCEE and PCA genres evident throughout.
It is given that in Genoa, 12 denarii make 1
soldi, 20 soldi, make 1 perns lire
(uncommon), and 1 perres of exchange =
5.67 lires (this was also used in the French
West Indies.
Page 15A
Addendum to MSS 399: American and Canadian Ciphering Books
80
circa
1820
BRIDGES,
Henry
M
152
12.75”
by 7.5”
Navigation,
Trigonometry,
Mensuration,
Spherical
Projection
81
circa
1820
POOR,
Jonathan
M
48
Arithmetic
82
18201830
HARADEN,
Andrew
(Aged 13)
M
36
83
circa
1821
SPOFFORD,
Mary
F
46
8.25”
by
6.5”
10” by
8.5”
(Printed
cover)
12.25”
by
7.5”
84
1822
PIERCE,
Nathan
M
108
85
©2009
1823
JENKINS,
Stephen
M
40
9.5 ” by
7.5”
9.5” by
7.5”
9.75”
by 8”
12.25”
by
7.75”
17.25”
by
10.25”
(huge)
Elementary
Arithmetic
Arithmetic
Arithmetic
Elementary
Geometry,
Trigonometry,
Gunter Scale,
Navigation
(logarithms
used
throughout)
High
(mature)
Beautiful
calligraphy,
elegant line
diagrams
Low
This is quite advanced in its presentation.
IRCEE genre is evident throughout. There is
no date in the m/s, but the m/s was donated
by Henry G. Bridges in 1916. We think that
this m/s was originally prepared by his father
(or, perhaps, grandfather).
Medium
Some underlining, in red ink.
Avoirdupois, weights
measures, decimals, Rules
of 3, inverse proportion,
compound proportion,
vulgar fractions, tare &
tret, barter, loss and gain,
alligation (M & A), S &
D position, APs and GPs
Decimals (single Rule of
Three), practice,
compound operations,
reduction, single Rule of
Three, inverse proportion,
compound proportion,
vulgar fraction
Medium/
high, faint,
meticulous
Advanced arithmetic for a female. Prepared
at Andover Academy, Andover, MA.
Straight-edge and
Compass constructions.
Calculating distances,
traverse sailing, parallel
sailing, middle latitude
sailing, Mercator’s
sailing. Log (probably
hypothetical) journey –
probably hypothetical –
from Boston to Madeira
(dated March 1808)
High
(Beautiful
colored
diagrams,
red ink
used for
ruling)
Numeration, 4 operations,
compound operations,
reduction, interest (S & C)
Compound operations,
decimals, reduction
High
On inside of soft covers there are
(Exquisite) commercially printed “necessary tables in
arithmetic”.
Perfect genre specimens: IRCEE and PCA.
Page 16A
Addendum to MSS 399: American and Canadian Ciphering Books
86
1823
TROVANT,
Charles S.
(from
Marshfield)
87
1824
Unidentified
88
1824
WARDWELL,
Abiel H.
89
circa
1825
90
32
12.25”
by
7.75”
Navigation
(logarithms
used
throughout)
42
12” by
7.5”
M
66
12.25:
by
7.5”
Elementary
Geometry,
Trigonometry,
Navigation
Elementary
Arithmetic
DAYTON,
Bela
F
72
12” by
7.25”
Arithmetic
1825
WOODBURY,
John
M
168
91
circa
1825
Unidentified
92
1826
DEY,
Richard
M
84)
93
1826
JORDAN,
Harrison G. O.
M
136
13.75”
by
8.25”
(48
pages)
and
12.75”
by
7.25”
(120
pages)
9.75”
by
7.75”
12.75”
by
7.75”
12” by
7.5”
and 13”
by 8.5”
©2009
M
48
Various forms of sailing –
plane, traverse, parallel,
middle latitude,
Mercator), Gunter’s scale,
log of journal (brief)
Various forms of sailing –
plane, traverse, parallel,
middle latitude, Mercator),
variations of the compass
Federal money, numeration, four operations,
measures, decimals,
miscellaneous questions,
bill of parcels, decimals
4 operations, compound
operations, measures,
reduction, decimals,
Federal money, interest (S
& C), Rule of Three
High
Beautiful water-color diagrams. The log
covers only 24 hours of sailing. There is a
reference to Nathan Bowditch’s text.
Marbled card covers.
Medium
Spelling is inconsistent – e.g., “sailing,”
“plane sailing,” “plain sailing” on different
pages. No covers; sewn as a quire.
Low/
medium
Hessian bag covers sewn in. Standard
IRCEE and PCA genres evident throughout.
Arithmetic
Standard sequence to
fellowship, vulgar
fractions, decimals,
practice, inverse
proportion, measures
(avoirdupois, troy, etc.)
Medium
Soft covers, rag paper, signatures sewn in.
Standard IRCEE and PCA genres evident
throughout.
Arithmetic
Rule of Three, fellowship
(S & D), interest (S & D),
and Federal money
Various kinds of sailing
were considered
Medium
Soft covers, commercially printed covers.
IRCEE and PCA genres evident throughout.
Low
This has a heavy, old card cover.
Medium
Fragile condition. The teacher referred to
work by H. G. O. Jordan, “practice by Cap
Elizabeth.”
Elementary
Navigation
Arithmetic
Rule of Three, compound
proportion, vulgar
fractions, miscellaneous
questions, practice, tare
and tret, fellowship (S &
Definitions, multiplication tables, etc., were
printed on the commercially prepared covers.
Plain, white card, with printed tables on the
inside.
Page 17A
Addendum to MSS 399: American and Canadian Ciphering Books
94
1829
Unidentified
95
circa
1829
HOOK,
Emeline A.
96
circa
1830
97
98
©2009
D), commission and
brokerage, insurance,
discount, equation of
payments, barter, loss and
gain, alligation (M & A),
double position,
involution and evolution,
APs and GPs,
permutations.
Standard approaches
throughout. Includes
“oblique trigonometry.”
47
13” by
8.5”
Trigonometry,
Navigation,
Surveying
F
42
7.5” by
6”
Elementary
Arithmetic
HOOKE,
Eliza
F
12
6.75”
by
5.25”
Geometry
Elementary geometry
theorems, with welldrawn diagrams.
circa
1830
PORTER,
Mary E.
F
48
13.75”
by
6.75”
Arithmetic
circa
1830
PRESTON,
Augustus
M
48
13.75”
by
6.75”
Arithmetic
Decimal fractions,
reduction, miscellaneous
examples, exchange of
currencies, simple
interest, equation of
payments, allowance for
leakage, custom house
business, proportion (not
called Rule of Three),
fellowship, chain rule,
loss and gain,
duodecimals, involution,
square and cube roots,
progressions (A & G)
Discount, equation of
payments, barter,
allegation (sic.), medial
loss and gain, single
position, progression
Medium
(Marbled
soft
covers)
Medium
Large calligraphic headings, some neat line
drawings. IRCEE genre throughout.
Lists of numbered solutions given (from a
book) E.g., 96. “Fifty thousand seven
hundred and five.” Answer is 50, 705.
Salem West School. Mature hand.
Medium/
high. Good
ink diagrams
and
calligraphic
headings
Medium/
There is a fair bit of explanation, not just
high
calculation.
Low/
medium
Headings, etc., are in normal calligraphic
mode, but the genre is different, in that
there is a lot of explanation, and not much
calculation.
Page 18A
Addendum to MSS 399: American and Canadian Ciphering Books
99
circa
1830
ROBINSON,
Fidelia
F
172
9” and
7.5”
and 10”
by 7.5”
Arithmetic
100
1831
JORDAN
H. G. A.
M.
40
13.5”
by 8.5”
Elementary
Geometry,
Trigonometry,
Navigation
(logarithms
used
throughout)
101
1835
HUTCHINSON,
Asa
(14 years old)
F
26
102
1836
SNOW,
James
M
48
©2009
Arithmetic
12” by
8”
Arithmetic
V1: Numeration,
measures, compound
operations
V2: Reduction, Federal
money, decimal fractions
V3: Practice, fellowship,
tare and tret, simple
interest, insurance, barter,
discount
V4: Rule of Three,
inverse proportion, vulgar
fractions.
Straight-edge/compass
constructions,
trigonometry (plane and
oblique), various types of
sailing (plane, traverse,
Mercator’s, parallel,
middle latitude)
Medium
Standard IRCEE and PAC genres evident
throughout. Each volume is sewn within
soft, commercially-produced covers. 4
Volumes.
Medium
Reduction, compound
division, decimals, vulgar
fractions, Rule of Three
(single), inverse
proportion
Reduction, vulgar
fractions, compound
operations, vulgar
fractions, simple interest,
partial payments,
discount, commission &
brokerage, compound
interest, equation of
payments, practice, proportion, chain rule, compound proportion, fellow-
Medium
IRCEE (but not PCA) genre evident
throughout. There was no log of a journal of
a trip in the m/s. This has wonderful,
commercially produced, soft covers, on
which advice details the following were
given: “To Make a Pen,” “Multiplication
Table,” “Pence Table,” “Shillings Table,:
“Addition and Subtraction Table,”
“Temperance Table,” “School Books and
Stationary.” The publishers Shirley and
Hyde announced that they sold arithmetics
by Walsh, Colburn, Kinne, Jackson,
Temple, Staniford, Welsh, Smith, Adams,
Root, and Weeks.
Several of the questions are solved by
algebra (in the mature hand of a teacher?)
Low/
medium
IRCEE and PCA genres very evident
throughout. The actual soft covers were
commercially sold.
Page 19A
Addendum to MSS 399: American and Canadian Ciphering Books
103
18371841
ROGERS,
Augustus D.
M
280
8” by
6.5”
104
18361837
JOHNSON,
Samuel
M
148
8” by
6.5”
105
18361837
JOHNSON,
Samuel
M
43
106
circa
1837
JOHNSON,
Samuel
M
185
107
circa
1840
DODGE,
Elizabeth
F
10
©2009
8” by
6.5”
Geometry,
Trigonometry,
Navigation,
Gauging,
Surveying
Arithmetic
Algebra
Geometry,
Trigonometry,
Mensuration,
Surveying,
Navigation
7” by
5”
Arithmetic
ship, loss and gain,
duodecimals, involution,
evolution, permutations,
double position.
Standard elementary
geometry construct-ions,
various types of sailing,
mensuration, gauging,
surveying
4 operations, compound
operations, duodecimals,
vulgar fractions, decimals,
reduction, Federal money,
circulating decimals,
proportion in general,
simple proportion, Rule of
Three, practice, tare and
tret, compound
proportion, fellowship (S
& D), alligation (medial
& alternate), involution,
evolution.
Miscellaneous questions,
linear equations, quadratic
equations, questions on
mensuration of superficies
and solids
Elementary axiomatic
geometry, navigation,
conic sections,
trigonometry, mensuration, surveying, spherical
trigonometry. Many of the
problems were probably
taken from some unnamed
textbook
This is really an exercise
book, in which solutions
to questions in Colburn’s
First Lessons are given.
Medium/
high
The hard cover has a “marbled” leather
spine cover. Medium/high penmanship and
calligraphy, with neat ink line diagrams.
Medium/
high
Standard IRCEE and PCA genres evident
throughout. Finishes with “The sum of four
numbers in arithmetical progression is 56,
…”
Interestingly, the oxen problem (from Isaac
Newton, and in Emerson’s Book 3) is
solved in this ciphering book – the correct
answer (36) to Newton’s original question
was obtained. The card cover was
commercially printed.
Low/
medium
See link to
www.harvardsquarelibrary.org/Heralds/Sam
uel-Johnson.php for a summary of the life
of Samuel Johnson.
High. Some
of the line
drawing, in
ink, is
magnificent
.
Samuel Johnson (1822-1882) was the son of
a Physician. Samuel went to Harvard at age
16, and became a Minister. There is a
possibility that this Geometry m/s could
have been his sister’s (i.e., Catherine
Johnson’s). Alternatively, she might have
used it after Samuel had originally prepared
it. Text written in two directions: front-toback includes 96 pages; back-to-front
includes 89 pages. Each section has blank
pages between problems.
This is not really a ciphering book, but
merely an exercise book in which solutions
to a few questions are presented.
Page 20A
Addendum to MSS 399: American and Canadian Ciphering Books
108
1841
DODGE,
Daniel P.
(of Topsfield
Grammar
School)
M
24
109
1842
BEAL,
Freeman G.
M
60
110
1853
ROPES,
Edward D.
M
21
Arithmetic
Questions from Benjamin
Greenleaf’s National
Arithmetic are answered.
These are concerned with
the 4 operations,
involution and evolution,
double position,
compound interest (e.g.,
p. 170, question 13), and
practice.
13” by
8”
Elementary
Geometry,
Trigonometry,
Navigation
Various Types of Sailing
Medium
(blue ink
used)
14” by
10”
Trigonometry,
Surveying,
Navigation
Various Types of Sailing
Medium/
high
This is not in standard genre. Although
there are a few explanations, mostly only
answers to set problem are presented. The
24 pages are in a commercially-sold
exercise book (“Tawndrow’s New and
Improved Writing Books) that was
published in Salem by John P. Jewett. T.
Tawndrow was “Professor of Penmanship
in the 3 public schools of Salem, MA). Page
173, “Divide the larger denominator by the
smaller and multiply the quotient by the
numerator, and so on through the whole, in
the same manner.”
This m/s has soft blue covers, commercially
printed and with a multiplication table on
the front. Logarithms were not used
Logarithms were used throughout the text.
IRCEE (but not PCA) genre evident
throughout. After the year 1853 was
printed, the expression “Bowditch School,
Ahem!” was also printed (it is unclear why,
but possibly the spirit of Bowditch pervaded
the course that Ropes experienced.)
Comments on Three Other Mathematics Manuscripts Held by Phillips Library, but not Included in the above Summary
In addition to the 114 historically significant manuscripts summarized in the above list we would wish to draw attention to the following
manuscripts held by the Phillips Library. Although these additional manuscripts do not satisfy our definitional requirements for a ciphering
book, they are of considerable importance in the history of navigation, mathematics and mathematics education in the United States of
America.
1. The “Author Unknown” 1692-1694 Manuscript (Box 11, Folder 1)
The first, and oldest, of these additional manuscripts was prepared by an unknown writer between 1692 and 1694. It has 29 pages, and
dimensions 12” by 7.5.” This is the oldest handwritten American document relating to navigation education or mathematics education that we
have ever seen and, clearly it should be regarded as extremely rare and important. The entries focus on navigation, astronomy, and surveying,
with references being made, for example, to the Gunter scale (which had been developed in England in the seventeenth century by Edmund
Gunter). Of potential historical significance is the fact that this 1692-1694 manuscript mainly comprises a log of an intended voyage from
©2009
Page 21A
Addendum to MSS 399: American and Canadian Ciphering Books
Salem to newfoundLand [sic]. The idea of training potential sailors and navigators to develop a log of a journey was part of the curriculum of
the Royal Mathematical School founded at Christ’s Hospital School in London in 1673 (see Coldham, 1990). There are many later
(eighteenth and nineteenth) handwritten manuscripts held by the Phillips Library in which students have recorded logs of actual, or
“intended,” journeys. The Phillips Library holds Christ’s Hospital ciphering books by Benjamin Raffles (1755) and James Janeway (1767) –
see summary details of these manuscripts in the above table – and both of these incorporate logs of journey. This 1692-1694 manuscript
provides evidence that this same idea had been transported to New England, even before the beginning of the eighteenth century. A careful
examination of the above table will indicate that this practice of including logs of real or intended journeys became an important component
of early navigation education in Salem.
Technically, this 1692-1694 manuscript does not fit within our definition of a “ciphering book,” for it does not feature an attempt at high
quality penmanship and calligraphic headings and there is no evidence that the standard IRCEE and PCA genres were recognized and applied
by the unknown writer. The manuscript mainly comprises entries for a log of an intended journey.
2. The “Author Unknown” 1707 Manuscript (Box 11, Folder 2)
This is the second oldest handwritten manuscript on navigation that has been located in Phillips Library. Unfortunately, once again, the
author is unknown. There are 22 pages, with dimensions 12.25” by 7.75.” The standard of penmanship and calligraphy is “medium,” and
some line drawings (in ink) are included. The emphasis is on solving geographical, sailing, and astronomy problems, and there is a log of a
journey. This 1707 manuscript does not fit within our definition of a “ciphering book,” for it does not feature either of the standard IRCEE
and PCA genres, and there is no systematic attempt to cover, systematically, part of a curriculum.
3. Jean le Measurier’s 1711 Manuscript (Box 11, Folder 3)
This manuscript comprises 60 handwritten pages (dimensions 11.75” by 7.5”). The main themes covered are navigation and astronomy
and, once again, there is a log of an intended journey – for a journey that was dated from July 11, 1711 (“by permission of God from Lizard to
Boston in New England, in good ship Success of Guernsey under the command of Captain George Guillaume …”). It is noted that “on
Thursday 29th we had a fresh gale of wind.” In fact, the expression “fresh gale of wind” can be found in the intended or real logs of journeys
in numerous ciphering books held by the Phillips Library. Altogether, there are seven pages of handwritten notes in the log relating to this
journey, and it is noted that the ship “arrived at Boston by the blessing of God.” There are logs for several other journeys, some apparently
real journeys, included in this manuscript. Many calculations are shown that relate to the present and future paths of the ships in which the
journeys took place. The standard of penmanship and calligraphy is medium to high, there being some beautiful line drawings in the
manuscript. This manuscript, and the 1692-1694 and 1711 manuscripts (see above), provide strong evidence that from the earliest days of
Salem, navigation education was strongly practical.
©2009
Page 22A
Addendum to MSS 399: American and Canadian Ciphering Books
An Addendum
In Robert Middlekauff’s (1963) book, Ancients and Axioms: Secondary Education in Eighteenth-Century New England, the author
included the following statement regarding ciphering books (which he termed “copybooks”).
Copybooks reveal much about curriculum and teaching. The libraries of Yale and Brown have a few, as do the Massachusetts,
Connecticut and Rhode Island Historical Societies. Others may be seen at the Forbes Library and the New Haven Colony Historical
Society. But the best collection, numbering several hundred navigation, surveying, arithmetic, and mathematical copybooks, is in the
Uncatalogued MSS in the Essex Institute. (p. 197)
After having sought out extant collections of ciphering books in public libraries and archives across the nation, we would agree with
Middlekauff that the collection held by the Phillips Library (formerly Essex Institute Library) is the largest and best held in a public
institution in the United States. Our work at Phillips Library led us to conclude that 110 satisfy our definition of a “ciphering book.” However,
we have not ruled out the possibility that further searching within the Phillips Library could add significantly to that number.
Cohen (1982) stated that there were about 60 ciphering books in a collection in the Harvard University Library, but our own searching
of ciphering books in the Houghton Library at Harvard University indicated that many of the ciphering books held by that Library originated
from Europe, and not from the United States of America. There is a collection of over 50 ciphering books held at the University of North
Carolina at Chapel Hill, and many of these originated from southern states (Doar, 2006). In May 2009 we examined the collection of at least
35 ciphering books held in the Clements Library, at the University of Michigan, and found that these mostly originated from within the
United States. There are about 25 ciphering books – originally prepared by persons living in Huguenot families in the eighteenth and
nineteenth centuries – held by the Huguenot Historical Society, 18 Broadhead Avenue, New Paltz, NY. Other than the collections mentioned
above, and our own privately-owned collection of about 200 ciphering books (of which, over 140 originated in the United States), we know
of no other collection of ciphering books with more than 20 ciphering books.
There are ciphering books prepared by students attending the Royal Mathematical School, Christ’s Hospital (London) in the eighteenth
century, held in the Phillips Library, in the Clements Library (at the University of Michigan), in the Houghton Library (at Harvard
University), and in our own (Ellerton and Clements) collection.
References
Cohen, P. C. (1982). A calculating people: The spread of numeracy in early America. Chicago: University of Chicago Press.
Coldham, P. W. (1990). Child apprentices in America from Christ’s Hospital, London, 1617-1778. Baltimore, MD: Genealogical Publishing
Co.
Doar, A. K. (2006). Cipher books in the Southern Historical Collection. Master of Science thesis, University of North Carolina at Chapel Hill.
(See Box 1 in MSS 399 for a copy of this document.)
Middlekauff, R. (1963). Ancients and axioms: Secondary education in eighteenth-century New England. New Haven, CT: Yale University
Press.
©2009
Page 23A