Hipparchus of Nicea publishes a catalog of stars that itself would be lost to history, but would form the basis of Ptolemy’s “Almagest.” Hipparchus also computed such as the length of the year, the motion of the sun and moon, and the precession of the equinoxes.

Several mathematical innovations were necessary for the completion of Hipparchus’ astronomical computations. Though many of the techniques and models employed are no longer used today, they form a basis for modern mathematics and positional astronomy.

Foremost among his achievements was his table of chords, one of the earliest forms of trigonometric tables. The table of chords would give the length of a chord of a circle if he knew the angle subtended by the chord from the center of the circle and the size of the circle. Modern trigonometry shows a direct lineage from this work.

Of note is the fact that his calculations were based on a geocentric model of the universe and the belief that bodies orbited in perfectly circular paths with irregularities accounted for by epicycles, circular motions along the existing circular path. That these beliefs were found to be untrue in no way detracts from the extraordinary accuracy of his work. The geocentric hypothesis was originally abandoned for philosophic and not computational reasons. The method of epicycles did not come into question until more accurate observations caused the need for further unwieldy layers of epicycle upon epicycle. The mathematics employed by Hipparchus was well suited to the computation of observed phenomena as seen from Earth with the instruments available.

Author: Paul D. Koenig

References:
Ball, W. W. Rouse. 1960. Short Account of the History of Mathematics. Mineola: Dover

Crowe, Michael. 1990. Theories of the World from Antiquity to the Copernican Revolution. Mineola: Dover.

Heath, Sir Thomas. 1960. Greek Mathematics vII. London: Oxford U Press

Hofmann, Joseph. 1957. History of Mathematics. New York: Philosophical Library

Thurston, Hugh. 1994. Early Astronomy. New York: Springer-Verlag