**The Greek astronomer Hipparchus (active 162-126 B.C.) discovered the precession of the equinoxes, founded trigonometry, and compiled the first star catalog.**

Born at Nicaea in Bithynia, Hipparchus studied astronomy, perhaps under Theodosius, and made some of his early observations in his native city. From at least 162 B.C. he was on the island of Rhodes, where he especially observed solstices, equinoxes, and lunar eclipses. His last recorded observation was made in 126 B.C. Hipparchus wrote on a variety of subjects connected with astronomy, but of his 14 works known once to have existed, only the commentary on Aratus's Phaenomena is extant. His astronomical work is known chiefly through the Almagest of Ptolemy and the writings of Strabo of Amisela.

Hipparchus seems to have initiated the study of plane trigonometry, devising for that purpose a table of chords of angles ranging from 0 to 180 °. He also developed a method of solving spherical triangles. By means of his trigonometric calculations he was able to determine, with greater accuracy than ever before, right and oblique ascensions and declinations, as well as simultaneous risings or settings of stars at different terrestrial latitudes. He also applied his methods to the solution of the problem of determining planetary positions. In his later years he drew up an elaborate catalog of 850 or more fixed stars, giving for each its longitude and latitude and also the apparent brightness, based on a system of six magnitudes similar to that used today.

## Precession of the Equinoxes

Hipparchus's greatest discovery was that of precession of the equinoxes, that is, the fact that the sun takes less time to return to the same solstitial or equinoctial point than it takes for the expiry of the sidereal year. He arrived at the discovery by a comparison of his own observations with those made earlier by Meton and Euctemon (432 B.C.) and Aristarchus (281 B.C.). He determined the annual amount of precession and from this obtained a nearly correct value for the duration of the tropical year (the period of the sun's rotation from equinox to equinox), which was too great by only 6 1/2 minutes.

## Planetary, Solar, and Lunar Studies

In planetary theory Hipparchus was undoubtedly familiar with the work done by earlier astronomers, and he combined many of their observations with his own but was unsuccessful in formulating a planetary theory. However, he did explain that there are two inequalities for each planet, that the retrogradations of each are variable in extent, and that these phenomena can be represented by combining earlier hypotheses of eccentric circles and epicycles on concentric circles.

With respect to the moon and sun, Hipparchus was indebted to the Babylonians, but he improved upon earlier estimates of the size and distance of the two bodies. Though he himself observed lunar eclipses, he also employed the data on two sets of three eclipses of 383-382 and 201-200. On the basis of his examination of one of these two sets, Hipparchus determined the radius of the lunar epicycle, and on the basis of his examination of the other set, he determined the eccentricity of the lunar orbit. That these factors were equal was a fact about which Hipparchus was well aware. Evidently Hipparchus tried to account only for the inequality in lunar motion, which is due to the elliptical form of the moon's orbit. In discussing lunar latitude, he used data from the eclipse of 502, derived from cuneiform sources; he determined the inclination of the lunar orbit to the ecliptic to be 5 °.

In devising a model to account for the inequity of solar motion, Hipparchus was more successful than with the planets and the moon. Brilliantly, by means only of estimates of the time between the vernal equinox and the summer solstice and of that between the summer solstice and the autumnal equinox, he proved that the apogee of the sun lies at Gemini 5;30 ° (5 ° 30 ′ ) and that the eccentricity of the solar orbit is 1/24 of the radius of the eccentric circle. His final work was the determination of the angular diameters and distances, in earth radii, of the sun and moon from the center of the earth. Though Ptolemy was able to improve on these parameters, the gross underestimation of the size of the solar system in antiquity could not be corrected before the 17th century.

## Geographical Work

Hipparchus's work on geography was a criticism, in three books, of Eratosthenes. In his discussion of Eratosthenes's geography he is concerned with mathematical errors in determining the latitudes of, and distances between, places. He evidently desired to establish a coordinate system of parallels of longitude and latitude for determining geographical positions, such as he employed for fixing the positions of the fixed stars. The data at his disposal, however, especially those concerning terrestrial longitude, were not sufficient to carry out his scheme. Fundamental to this effort was his estimate, based on Eratosthenes's value for the circumference of the earth (252, 000 stades), that 1 ° of either longitude or latitude on the earth's surface is equal to a distance of 700 stades.

## Influence of Hipparchus

Hipparchus was a careful and cautious scientist who prepared the way for those who followed him by establishing a high standard of observational astronomy, by devising trigonometrical methods of solving problems in mathematical astronomy, and by collecting and criticizing the observational material of his predecessors, both Babylonian and Greek. Like many another, his greatest achievement was to make it possible for his successors to eclipse him and relegate his works to oblivion.

## Further Reading on Hipparchus

There is no comprehensive work on Hipparchus, but a good biography is in Henry Smith Williams, The Great Astronomers (1930). None of the discussions of his astronomical work in the standard histories of science is adequate. There is a brief discussion in J. L. E. Dreyer, A History of Astronomy from Thales to Kepler (rev. ed. 1953). A general survey of Hipparchus's life and an appreciation of his achievements, along with a detailed study of the fragments of his criticism of Eratosthenes, is in D. R. Dicks, ed., The Geographical Fragments of Hipparchus (1960).