His theory of the planets was not so complete, for there was no sufficient body of ancient observations to be compared with those which he himself accumulated with so much diligence. Considering the data at his disposition and the use made of them, the work of Hipparchus is of the first order. Astronomers of all ages are agreed that he was 'one of the most extraordinary men of antiquity; the very greatest in the sciences that require a combination of observation with geometry' (Delambre).
His expositor, Ptolemy of Alexandria, was primarily a geometer and made few original observations. The Almagest is, in essence, a restatement of the theories of Hipparchus with additions, not all of which are improvements. It begins by laying down certain postulates: The earth is spherical and a mere point in respect of the heavens; its circumference is 180,000 stadia; the heavens are likewise spherical and revolve about the earth, which is in the center and has no motion. So far he is in agreement with Aristotle. Where he differs, astronomers who succeeded him followed the Almagest while philosophers were more apt to take Aristotle as authority.
Ptolemy's theory of the moon's motion led him to important discoveries, which need not be described here. It is mentioned because it also contained a contradiction of the precise sort that is best suited to lead to further discoveries, and because this contradiction was passed over and entirely neglected by him and by his successors for centuries. His theory gave the position of the moon with satisfactory accuracy. It was, in so far, presumably true. It assumed that at times the moon was twice as far from the earth as at others. If this were true the moon's apparent diameter should sometimes have been twice as great as at other times. But no such variation was observed. The necessary conclusion: Hence the theory can not possibly be true—was not drawn by Ptolemy. The instance is significant; it marks a radical difference between the modern attitude and that of the ancients in matters of physical science. Ptolemy and his successors really held two antagonistic theories of the moon's motion and distance at the same time. Each theory satisfied the conditions of part of the problem. They did not seek for a unique theory. This was not done until the time of Kepler, whose whole life was spent in searching for the physical causes of observed phenomena, and who was not content with mere analytic devices by which the phenomena could be predicted. He sought for these, but he looked deeper and further.
All but a few of the greatest of the ancients regarded a physical problem in the light of a riddle to which an answer was required. Any plausible answer would do. The fixed belief that there was one answer and could be only one did not arise till quite modern times. Modern science is a search for such unique solutions. Most of ancient science was a search for an hypothesis to account for a set of observed facts.
