ASTRONOMY 175 



and eccentrics which will account for the facts 

 observed. 



Hipparchus acquitted himself of this task in a 

 masterly fashion. He not only succeeded in sur- 

 mounting the difficulties which had arrested his pre- 

 decessors, but he discovered new facts such as the 

 precession of the equinoxes and gave a geometrical 

 explanation of them. 1 



Inspired by the conceptions of Hipparchus, Ptolemy 

 summarized and completed the astronomical know- 

 ledge of antiquity in the form in which it was be- 

 queathed to the Middle Ages. At this period, two 

 tendencies manifested themselves : one amongst the 

 Arabs, the other amongst scholastic thinkers. 



The Arabs could not be satisfied with the abstract 

 conceptions of Greek astronomers ; they sought un- 

 dauntedly to materialize the geometrical fictions, and 

 to give them a physical basis. " In reality," said 

 Averroes, " the astronomy of our time does not exist ; 

 it is suitable for calculation, but does not agree with 

 what really is." 2 To fill this gap Al-Bitrogi imagined 

 nine solid and transparent spheres and attempted to 

 explain all the celestial phenomena by their arrange- 

 ment. 3 This realistic conception found favour in the 

 Middle Ages. As Paradise was situated at the outer- 

 most part of the heavens, in order to reach it it was 

 necessary to cross the solid spheres by certain fixed 



1 He ignored the physical cause of this phenomenon, namely 

 the equatorial bulging of the earth. In consequence of this 

 bulging, the earth in its movement of rotation moves like an 

 oscillating spinning-top, therefore the plane of the equator 

 and the plane of the ecliptic do not intersect at the same point 

 at the end of an annual revolution. The result is that after 

 each year the sun returns to the equinox slightly sooner than 

 it otherwise would do with respect to a star taken as a guiding 

 mark of reference. 



2 13 Duhem, Systenie II, p. 139. 



3 Ibid., p. 149. 



