172 SCIENCE IN GRECO-ROMAN ANTIQUITY 



the latter and combines this with its own uniform 

 movement. 



Things proceed in this manner down to the last 

 sphere, which carries the planet on its equator, and as 

 many spheres are required as there are particular 

 movements of the planet to explain. 



For instance, if the plane of the moon were the same 

 as that of the ecliptic, there would be as many eclipses 

 of the sun and moon as there are new and full moons, 

 and two spheres would be sufficient to account for the 

 observed facts. But the plane of the moon being 

 inclined to that of the ecliptic, the latter is cut by the 

 lunar orbit at two points or nodes, at which points 

 alone eclipses can take place. As these nodes are dis- 

 placed by a uniform and regular movement, it requires 

 a special sphere to explain this displacement. So that 

 three spheres in all are necessary to explain the move- 

 ment of the moon in the heaven. 



The problem is more complicated where the planets 

 are concerned, since here there are stationary points 

 and retrogradations followed by new progressions. 

 Thus for each planet Eudoxus had recourse to four 

 spheres : the first is connected with the diurnal revolu- 

 tion, the second with the zodiacal revolution, the third 

 and fourth with the irregular movements. 



There would be in all 27 spheres (20 for the planets, 

 three for the sun, three for the moon, and one for the 

 stars) . 



Aristotle adopted the system of Eudoxus and sought 

 to perfect it, partly by his own ideas and partly by 

 those of Calippus. In the system of Eudoxus the 

 movement of each planet forms an independent whole. 

 Aristotle imagined compensating spheres which are 

 intercalated in the spaces between the various 

 mechanisms of the heavenly bodies. All the move- 

 ments of the planets then become one with the single 

 movement which animates the starry sphere. Aristotle 



