INDUCTIVE EPOCH OF HIPPARCHUS. 153 



terms, or expressions of partial motions ; and these terms involve sines 

 and cosines, that is, certain technical modes of measuring circular mo 

 tion, the circular motion having some constant relation to the time. 

 And thus the problem of the resolution of the celestial motions into 

 equable circular ones, which was propounded above two thousand 

 years ago in the school of Plato, is still the great object of the study 

 of modern astronomers, whether observers or calculators. 



That Hipparchus should have succeeded in the first great steps of 

 this resolution for the sun and moon, and should have seen its appli- 

 cability in other cases, is a circumstance which gives him one of the 

 most distinguished places in the roll of great astronomers. As to the 

 charges or the sneers against the complexity of his system, to which 

 we have referred, it is easy to see that they are of no force. As a 

 system of calculation, his is not only good, but, as we have just said, 

 in many cases no better has yet been discovered. If, when the actual 

 motions of the heavens are calculated in the best possible way, the 

 process is complex and difficult, and if we are discontented at this, 

 nature, and not the astronomer, must be the object of our displeasure. 

 This plea of the astronomers must be allowed to be reasonable. " We 

 must not be repelled," says Ptolemy, 12 "by the complexity of the 

 hypotheses, but explain the phenomena as well as we can. If the 

 hypotheses satisfy each apparent inequality separately, the combination 

 of them will represent the truth ; and why should it appear wonderful 

 to any that such a complexity should exist in the heavens, when we 

 know nothing of their nature which entitles us to suppose that any in- 

 consistency will result ?" 



But it may be said, we now know that the motions are more simple 

 than they were thus represented, and that the Theory of Epicycles was 

 false, as a conception of the real construction of the heavens. And to 

 this we may reply, that it does not appear that the best astronomers 

 of antiquity conceived the cycles and epicycles to have a material 

 existence. Though the dogmatic philosophers, as the Aristotelians, 

 appear to have taught that the celestial spheres were real solid bodies, 

 they are spoken of by Ptolemy as imaginary ; 13 and it is clear, from 

 his proof of the identity of the results of the hypothesis of an eccentric 

 and an epicycle, that they are intended to pass for no more than geo- 

 metrical conceptions, in which view they are true representations of 

 Ihe apparent motions. 



12 Synt. xiii. 2. " Ibid. iii. 3. 



