number required by Aristotle reaching fifty-five.  It may be regarded as counting in Aristotle’s favour that he did consider the earth to be a sphere and not a flat disc, but he seems to have thought that the mathematical spheres of Eudoxus had a real solid existence, and that not only meteors, shooting stars and aurora, but also comets and the milky way belong to the atmosphere.  His really great service to science in collating and criticising all that was known of natural science would have been greater if so much of the discussion had not been on the exact meaning of words used to describe phenomena, instead of on the facts and causes of the phenomena themselves.

Aristarchus of Samos seems to have been the first to suggest that the planets revolved not about the earth but about the sun, but the idea seemed so improbable that it was hardly noticed, especially as Aristarchus himself did not expand it into a treatise.

About this time the necessity for more accurate places of the sun and moon, and the liberality of the Ptolemys who ruled Egypt, combined to provide regular observations at Alexandria, so that, when Hipparchus came upon the scene, there was a considerable amount of material for him to use.  His discoveries marked a great advance in the science of astronomy.  He noted the irregular motion of the sun, and, to explain it, assumed that it revolved uniformly not exactly about the earth but about a point some distance away, called the “excentric".[1] The line joining the centre of the earth to the excentric passes through the apses of the sun’s orbit, where its distance from the earth is greatest and least.  The same result he could obtain by assuming that the sun moved round a small circle, whose centre described a larger circle about the earth; this larger circle carrying the other was called the “deferent”:  so that the actual motion of the sun was in an epicycle.  Of the two methods of expression Hipparchus ultimately preferred the second.  He applied the same process to the moon but found that he could depend upon its being right only at new and full moon.  The irregularity at first and third quarters he left to be investigated by his successors.  He also considered the planetary observations at his disposal insufficient and so gave up the attempt at a complete planetary theory.  He made improved determinations of some of the elements of the motions of the sun and moon, and discovered the Precession of the Equinoxes, from the Alexandrian observations which showed that each year as the sun came to cross the equator at the vernal equinox it did so at a point about fifty seconds of arc earlier on the ecliptic, thus producing in 150 years an unmistakable change of a couple of degrees, or four times the sun’s diameter.  He also invented trigonometry.  His star catalogue was due to the appearance of a new star which caused him to search for possible previous similar phenomena, and also to prepare for checking future ones.  No advance was made in theoretical