The reasons which weighed with Hipparchus were presumably the facts that the system in which the earth revolved in a circle of which the sun was the exact _centre_ failed to “save the phenomena,” and in particular to account for the variations of distance and the irregularities of the motions, which became more and more patent as methods of observation improved; that, on the other hand, the theory of epicycles did suffice to represent the phenomena with considerable accuracy; and that the latter theory could be reconciled with the immobility of the earth.
Archimedes tells us in the same treatise that “Aristarchus discovered that the sun’s apparent size is about 1/720th part of the zodiac circle”; that is to say, he observed that the angle subtended at the earth by the diameter of the sun is about half a degree.
ON THE SIZES AND DISTANCES OF THE SUN AND MOON.
Archimedes also says that, whereas the ratio of the diameter of the sun to that of the moon had been estimated by Eudoxus at 9 : 1 and by his own father Phidias at 12 : 1, Aristarchus made the ratio greater than 18 : 1 but less than 20 : 1. Fortunately we possess in Greek the short treatise in which Aristarchus proved these conclusions; on the other matter of the apparent diameter of the sun Archimedes’s statement is our only evidence.
It is noteworthy that in Aristarchus’s extant treatise _On the sizes and distances of the sun and moon_ there is no hint of the heliocentric hypothesis, while the apparent diameter of the sun is there assumed to be, not ½°, but the very inaccurate figure of 2°. Both circumstances are explained if we assume that the treatise was an early work written before the hypotheses described by Archimedes were put forward. In the treatise Aristarchus finds the ratio of the diameter of the sun to the diameter of the earth to lie between 19 : 3 and 43 : 6; this would make the volume of the sun about 300 times that of the earth, and it may be that the great size of the sun in comparison with the earth, as thus brought out, was one of the considerations which led Aristarchus to place the sun rather than the earth in the centre of the universe, since it might even at that day seem absurd to make the body which was so much larger revolve about the smaller.
