TEE PREDECESSORS OF COPERNICUS. 323 



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 accrnnulated with so much diligence. Considering the 

 data at his disposition and the use made of them, the work of Hip- 

 parchus 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 dis- 

 coveries, 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 pre- 

 dicted. 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. 



