96 SCIENCE IN GRECO-ROMAN ANTIQUITY 



full of air is lighter than an empty bladder. His Optics, 

 of which the first book has been preserved to us in a 

 laborious translation from Arabic into Latin, treats not 

 only of perspective as Euclid had done, but also of the 

 physical conditions of vision and of optical illusions, and 

 here Ptolemy accepts the theory of Plato that visual per- 

 ception is produced by the rays proceeding from the 

 eye meeting those proceeding from the object. In his 

 Catoptrics he studies mirrors, and by measurements 

 seeks to establish the law of angles of incidence and 

 reflection. He also made comparative experiments 

 on refraction in water and glass, and ascertained the 

 existence of an astronomical refraction, the distance 

 from a star to the pole being smaller when the star is on 

 the horizon than when it passes the meridian. The 

 figures found are not always accurate, but the experi- 

 ments and ideas remain none the less of prime import- 

 ance. Another work, more important still, was the 

 one which Ptolemy devoted to astronomy. It was 

 soon used as a text-book in the schools of Alexandria, 

 and in order to distinguish it from similar but much 

 smaller works, it was given the title of " jjfieyioTt]," 

 the greatest (book understood), which translated into 

 Arabic became corrupted into Almagest. 1 The work 

 is divided into 13 books. In the first, Ptolemy gives 

 an exposition of plane and spherical trigonometry and 

 a table of chords. The second book discusses the 

 phenomena arising from the spherical shape of the 

 earth, with the admission that the hypothesis, which 

 he rejects, of the revolution of the earth round its axis, 

 would greatly simplify the explanations. Books III— 

 VI treat of the movements of the sun and moon and 

 of eclipses, all explained by means of epicycles and 

 eccentrics. Books VII-VIII contain the catalogue of 

 Hipparchus, completed and enlarged. The last books 

 enumerate the sidereal phenomena which occur every 

 1 15 Heiberg, Natuvwiss., p. 82. 



