DECLINE OF ALEXANDRIAN SCIENCE 129 



In Books III, IV, and V, Ptolemy discusses the apparent motions 

 and distances of the sun and moon by means of excentrics and 

 epicycles, his method for determining the moon's distance being 

 substantially the same as the modern. Book V describes the con- 

 struction and use of his chief instrument, the astrolabe. Book VI" 

 deals with eclipses, using a value of TT equivalent to our 3.1416. 

 He determines the distance of the sun, following Hipparchus, by 

 observing the breadth of the earth's shadow when the moon 

 crosses it at an eclipse. Books VII and VIII contain a catalogue 

 of 1028 stars based on that of Hipparchus, and a discussion of 

 precession of the equinoxes, with a close determination of the 

 unequal intervals between successive vernal and autumnal equi- 

 noxes. The remainder of the treatise is devoted to the planets, 

 containing Ptolemy's chief original contributions. 



While Ptolemy did not take advantage of the better data at 

 his command to improve the theory of the sun's motion, he did 

 make substantial progress with that of the moon, the discrepancies 

 for which rarely exceed 10', which represented about the maximum 

 precision of his instruments. Hipparchus had assumed the moon 

 to have a motion representable by one circle with the earth as a 

 centre and by an epicycle with its centre upon this. Discrepancies 

 between observed and computed positions led Ptolemy, bound asv 

 he was by the Aristotelian dictum that celestial bodies can move 

 only in circular paths, to modify this by making the first circle 

 excentric to the earth, the line joining the centres of the circle 

 and the earth being itself assumed to revolve. This theory, while 

 giving results of sufficient accuracy for the observations at certain 

 positions of the moon, exaggerated considerably the variation of 

 its distance from the earth, making this at times almost twice 

 as great as at others. 



For the five planets, or "wandering stars," he also assumed ex- 

 centric deferents, and as a further means of accounting for dis- 

 crepancies, an additional point, in line with the centres of earth and 

 deferent, called the "equant," with respect to which the centre of 

 the epicycle would have uniform angular velocity. The planes of 

 the epicycles were slightly inclined to that of the ecliptic. 



