Fifty years after Apollonius, B.C. 160-125, we meet with the great astronomer Hipparchus. He does not appear to have made observations himself in Alexandria, but he uses those of Aristyllus and Timochares of that place. Indeed, his great discovery of the precession of the equinoxes was essentially founded on the discussion of the Alexandrian observations on Spica Virginis made by Timochares. In pure mathematics he gave methods for solving all triangles plane and spherical: he also constructed a table of chords. In astronomy, besides his capital discovery of the precession of the equinoxes just mentioned, he also determined the first inequality of the moon, the equation of the centre, and all but anticipated Ptolemy in the discovery of the evection. To him also must be attributed the establishment of the theory of epicycles and eccentrics, a geometrical conception for the purpose of resolving the apparent motions of the heavenly bodies, on the principle of circular movement. In the case of the sun and moon, Hipparchus succeeded in the application of that theory, and indicated that it might be adapted to the planets. Though never intended as a representation of the actual motions of the heavenly bodies, it maintained its ground until the era of Kepler and Newton, when the heliocentric doctrine, and that of elliptic motions, were incontestably established. Even Newton himself, in the 37th proposition of the third book of the "Principia," availed himself of its aid. Hipparchus also undertook to make a register of the stars by the method of alineations--that is, by indicating those which were in the same apparent straight line. The number of stars catalogued by him was 1,080. If he thus depicted the aspect of the sky for his times, he also endeavoured to do the same for the surface of the earth by marking the position of towns and other places by lines of latitude and longitude. [Sidenote: The writings of Ptolemy.] [Sidenote: His great work: the mechanical construction of the heavens.]