DECLINE OF ALEXANDRIAN SCIENCE 127 



that the retrogradations of each are variable in extent, while the other 

 mathematicians had only demonstrated geometrically a single in- 

 equality and a single arc of retrograde motion ; and he believed that 

 these phenomena could not be represented by excentric circles nor by 

 epicycles carried on concentric circles, but that, it would be necessary 

 to combine the two hypotheses. Dreyer. 



The instruments used by Ptolemy for his astronomical observa- 

 tions included :-- the "Ptolemaic rule," consisting of a rod with 

 sights pivoted to a vertical rod, the angle at the junction being 

 measured by the subtended chord ; the armillary circle, a copper 

 or bronze ring marked in degrees and mounted in the meridian 

 plane on a post. A second movable ring is fitted into this with 

 pegs diametrically opposite each other, by means of which the sun's 

 midday height could be measured ; the armillary sphere, similar in 

 principle but somewhat more complicated ; the astrolabe or as- 

 tronomical ring for measuring either horizontal or vertical angles. 

 Like the Chaldeans Ptolemy also used meridian quadrants of 

 masonry. Time was still measured by the flow of water, with 

 apparatus considerably improved by Ctesibus and Hero. The 

 numerous observations of Ptolemy were made during the period 

 125-151 A.D. and he was in Alexandria in 139. 



One of his observations he describes as follows : 



In the 2d year of Antoninus, the 9th day of Pharmonthe, the 

 sun being near setting, the last division of Taurus being on the 

 meridian (that is, 5 equinoctial hours after noon), the moon was in 

 3 degrees of Pisces, by her distance from the sun (which was 92 de- 

 grees, 8 minutes) ; and half an hour after, the sun being set, and 

 the quarter of Gemini on the meridian, Regulus appeared, by the 

 other circle of the astrolabe, 57 degrees more forwards than the moon 

 in longitude. Whewell. 



THE ALMAGEST. - - In his celebrated Syntaxis, better known 

 from Arabic translations as the Almagest, Ptolemy undertakes to 

 present for the first time the whole astronomical science of his age. 



In Book I he reviews the fundamental astronomical data thus : 



