168 SCIENCE IN GRECO-ROMAN ANTIQUITY 



the fundamental distinction between the diurnal 

 motion and the annual retrogradation of the planets, 

 sun and moon, movement and retrogradation which 

 take place on two planes and about two different poles. 

 The Timaeus shows us the Demiurge who, after having 

 created a world-soul, cuts it in the shape of a X, 

 then curves back the extremities of this X so as to 

 obtain two circles. One of these circles represents the 

 equator and the uniform changeless movement of the 

 diurnal revolution ; the other represents the ecliptic 

 and the varied movements of the celestial bodies other 

 than the stars. 



The two circles are found again in the movements of 

 the mind, which sometimes seeks after the eternal, some- 

 times, on the contrary, clings to the changing elements 

 of reality. But the principal idea of the Pythagorean 

 astronomy, which Plato kept, was the opposition 

 between real and apparent movements. For this 

 reason, he assigns to astronomy the following task : to 

 account for these appearances, that is, to discover 

 behind the sensible phenomena the geometrical reasons 

 which explain and justify them. " Plato, says Sim- 

 plicius in his Commentaries (in Aristotelis libros de 

 coelo commentarii, Bk. II, cap. xii, Karsten edit., p. 219, 

 col. a), admits in principle that the celestial bodies 

 move with a circular motion, uniform and constantly 

 regular (that is, in the same direction) ; he propounds 

 therefore this problem to mathematicians — What are 

 the circular and perfectly regular movements which 

 may properly be taken as hypotheses to account for 

 the appearances of the wandering heavenly bodies ? " x 



The problem having been thus stated, it is necessary, 

 starting from Plato, to distinguish in Greek astronomy 

 two kinds of hypotheses which until that time had 

 been more or less mingled : the physical hypotheses 

 regarding the nature and constitution of the stars, and 

 1 Quoted from 13 Duhem, Systeme I, p. 103. 



