## Hipparchus

Hipparchus, who lived in the second century BC,1 built an observatory and performed most of his work on the island of Rhodes and was perhaps the greatest astronomer of antiquity. He used observations to produce geometrical models with real quantitative predictive power. His theory of the motion of the

Sun was extremely accurate and he produced a model for the Moon that worked well at new and full moons, thus enabling him to produce a theory of eclipses which, in the case of lunar eclipses, was very successful.

All of Hipparchus' works are lost except for his relatively unimportant Com2

mentary on the Phaenomena of Eudoxus and Aratus, though Ptolemy quotes his work often, sometimes verbatim. We also know of Hipparchus' work on the Sun through an introduction to astronomy written in AD first century by Geminus of Rhodes. Part of the reason for the lack of extant work by Hipparchus may well be the fact that Ptolemy's subsequent writings superseded those of his predecessor so totally, just as the existence of Euclid's Elements rendered obsolete all previous works on geometry.

Hipparchus attempted to use the eccentric circles and epicycles of Apollonius to develop models for the motion of the heavenly bodies that, in contrast to Babylonian theories, would enable future positions to be calculated for all times. For the Sun and the Moon he found that he could use just one such device, but for the planets he needed to combine the two. He was a great

1 Ptolemy refers to observations made by Hipparchus between 161 and 126 BC. In about 275 BC, Aratus of Soli wrote a very popular poem (the Phaenomena, inspired by a more technical, but now lost, work of Eudoxus) describing the risings and settings of stars and weather signs in both heavenly and natural phenomena. It was later translated into Latin and remained widely read for over 1000 years. Kidd (1997) contains a translation and commentary.

observational astronomer who improved the design of the instruments used for observing the skies and used these instruments to compile a catalogue of about 850 stars.

As we have seen, quantitative calculations that arose from astronomical problems often involved the solution of triangles, and it was for this reason that the subject of trigonometry developed. In fact, trigonometry did not become a branch of mathematics separate from astronomy until the fifteenth century. Hipparchus, who is considered to be the founder of trigonometry, constructed a table of chords (equivalent to a table of sines) though we do not know how

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