PRELUDE TO THE EPOCH OF HIPPARCHUS. 143 



real motions of the heavenly bodies must be circular and uniform. 

 The Pythagoreans, as well as the Platonists, maintained this dogma. 

 According to Geminus, "They supposed the motions of the sun, and 

 the moon, and the five planets, to be circular and equable : for they 

 would not allow of such disorder among divine and eternal things, as 

 that they should sometimes move quicker, and sometimes slower, and 

 sometimes stand still ; for no one would tolerate such anomaly in the 

 movements, even of a man, who was decent and orderlv. The occa- 

 sions of life, however, are often reasons for men going quicker or 

 slower, but in the incorruptible nature of the stars, it is not possible 

 that any cause can be alleged of quickness and slowness. Whereupon 

 they propounded this question, how the phenomena might be repre- 

 sented by equable and circular motions." 



These conjectures and assumptions led naturally to the establish- 

 ment of the various parts of the Theory of Epicycles. It is probable 

 that this theory was adopted with respect to the Planets at or before 

 the time of Plato. And Aristotle gives us an account of the system 

 thus devised. 7 " Eudoxus," he says, "attributed four spheres to each 

 Planet : the first revolved with the fixed stars (and this produced the 

 diurnal motion); the second gave the planet a motion along the 

 ecliptic (the mean motion in longitude) ; the third had its axis perpen- 

 dicular 8 to the ecliptic (and this gave the inequality of each planetary 

 motion, really arising from its special motion about the sun); the 

 fourth produced the oblique motion transverse to this (the motion in 

 latitude)." He is also said to have attributed a motion in latitude 

 and a corresponding sphere to the Sun as well as to the Moon, of 

 which it is difficult to understand the meaning, if Aristotle has report- 

 ed rightly of the theory ; for it would be absurd to ascribe to Eudoxus 

 a knowledge of the motions by which the sun deviates from the ecliptic. 

 Calippus conceived that two additional spheres must be given to the 

 sun and to the moon, in order to explain the phenomena : probably 

 he was aware of the inequalities of the motions of these luminaries. 

 He also proposed an additional sphere for each planet, to account, we 

 may suppose, for the results of the eccentricity of the orbits. 



The hypothesis, in this form, does not appear to have been reduced 

 to measure, and was, moreover, unnecessarily complex. The resolution 



7 Metaph. xi. 8. 



8 Aristotle says " has its poles in the ecliptic," but this must be a mistake of his. 

 He professes merely to receive these opinions from the mathematical astronomers, 



' f«c Trjs olKUOT&rrii <pi\oao<ptas tuiv iiadripaTiKwv. 



