64 A Short History of Astronomy [Cn. n. 



in addition to dealing more fully with the parts in which 

 Ptolemy made important advances. 



The Almagest consists altogether of 13 books. The 

 first two deal with the simpler observed facts, such as the 

 daily motion of the celestial sphere, and the general 

 motions of the sun, moon, and planets, and also with a 

 number of topics connected with the celestial sphere and 

 its motion, such as the length of the day and the times 

 of rising and setting of the stars in different zones of the 

 earth ; there are also given the solutions of some important 

 mathematical problems,* and a mathematical tablet of 

 considerable accuracy and extent. But the most interest- 

 ing parts of these introductory books deal with what may 

 be called the postulates of Ptolemy's astronomy (Book I., 

 chap. ii.). The first of these is that the earth is spherical; 

 Ptolemy discusses and rejects various alternative views, 

 and gives several of the usual positive arguments for a 

 spherical form, omitting, however, one of the strongest, 

 the eclipse argument found in Aristotle ( 29), possibly 

 as being too recondite and difficult, and adding the 

 argument based on the increase in the area of the earth 

 visible when the observer ascends to a height. In his 

 geography he accepts the estimate given by Posidonius 

 that the circumference of the earth is 180,00* stadia. The 

 other postulates which he enunciates and for which he 

 argues are, that the heavens are spherical and revolve like 

 a sphere ; that the earth is in the centre of the heavens, 

 and is merely a point in comparison with the distance of 

 the fixed stars, and that it has no motion. The position 

 of these postulates in the treatise and Ptolemy's general 

 method of procedure suggest that he was treating them, not 

 so much as important results to be established by the best 

 possible evidence, but rather as assumptions, more pro- 

 bable than any others with which the author was acquainted, 

 on which to base mathematical calculations which should 

 explain observed phenomena.* His attitude is thus 



* In spherical trigonometry. 



f A table of chords (or double sines of half-angles) for every ^ 

 from o to 1 80. 



\ His procedure may be compared with that of a political 

 economist of the school of Ricardo, who, in order to establish some 



