Hipparchus and Trigonometry

According to Gerald Toomer, Hipparchus (fl. 2nd century BC) founded trigonometry, by computing the first trigonometric function, namely, a chord table. However, Toomer is careful to explain that there was no ancient term for trigonometry, 'since it was not counted as a branch of mathematics' in antiquity. Rather, trigonometry was ancillary to astronomy. (There are various ancient classifications of mathematics. For example, the four 'Pythagorean sisters' included arithmetic, geometry, harmonics, and astronomy. Plato, in the Republic Book 7, also discussed the study of stereometry as part of the mathematical curriculum necessary for philosopher-kings.)

Toomer credits Hipparchus with the introduction of trigonometric functions in the form of a chord table, to solve the problem of the computation of specific positions from geometric models. With his chord table, Hipparchus could solve the problems of plane trigonometry. Toomer suggests that 'this was probably computed for a circle with radius 3438' (i.e. 360 degrees over 2 pi), and is 'the ancestor of a sine table found in ancient Indian astronomical works'. (No sine function has been found in Greek, but Toomer believes that this may have been derived by Indian mathematicians using Hellenistic astronomical works which are now lost.)

Recommended Reading

Toomer, G.J. "Hipparchus" in Oxford Classical Dictionary, 3rd ed. Oxford 1996

Toomer, G.J. "Trigonometry" in Oxford Classical Dictionary, 3rd ed. Oxford 1996

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