Answering a question:!
Where did the word “hypotenuse” come
from?!
Question about the question!
•  Is the question referring to “hypotenuse”
itself or its predecessors?!
Definitions!
•  American Heritage Dictionary: indicates the
Latin is hypotenusa and the Greek
hupoteinousa!
•  Merriam-Webster: Latin - hypotenusa; Greek
- hypoteinousa (from feminine: hypoteinon)!
•  “hypotenuse” is probably a translation of one
of these words.!
Origin of hypotenuse
Google vs. Bing!
•  Dr. Math!
•  reference.com
describes Greek
derivation: hypo(under), teinein (to
stretch)!
•  wordnik.com!
•  Dr. Math!
•  dictionary.reference.
com puts origin
1565 - 1575!
•  yourdictionary.com!
History of Math website!
•  Tried looking for mathematicians
between 1565 - 1575!
•  Robert Recorde (1510 - 1558)!
–  Translated an annotated version of Euclidʼs
Elements!
–  English!
Mathematicians between
1565 - 1575!
•  About 20 who would qualify!
•  Looking for an English dude - John Dee!
John Dee!
•  1527 - 1609!
•  Studied astronomy, astrology,
mathematics, coding, magic!
•  In 1570, edited a translation of Euclidʼs
Elements by Billingsley!
•  Could it be?!
Henry Billingsley!
•  No biography on trusty
History of Math website!
•  Title page of his
translation (Euclid of
Megara - wrong Euclid)!
•  Math forum indicates
information about
Billingsley is from Sir
Thomas Heath!
Sir Thomas Heath!
•  Created THE authoritative translation of
Euclidʼs Elements (details forthcoming)!
•  Describes all the translations up to his
point in time!
•  Confirms Billingsleyʼs 1570 translation!
•  According to Heath this is the earliest
English translation.!
Inference time (out of time)!
•  Hypotenuse seems to be the English
version of the Latin or Greek word!
•  A hypotenuse is the longest side of a
right-triangle (the common definition)!
•  Euclidʼs Elements dealt with right
triangles.!
•  English + Euclid = hypotenuse!
Next steps!
•  Heath does not explicitly say that
“hypotenuse” was used by Billingsley.!
•  We do not know that Recorde did not
include the term in his work.!
•  Need to find these works and
investigate further.!
•  HOLD THE PHONE. . . !
Sources!
•  http://www-history.mcs.st-and.ac.uk!
•  http://mathforum.org/geometry/
wwweuclid/billing.htm !
•  Heath, Sir Thomas (1947). Euclid The
Elements, Vol I. Ann Arbor, MI:
Cambridge University Press!