THE GRECO-ROMAN PERIOD 97 



year. A set of well-arranged astronomical tables 

 enables the time and eclipses to be determined accord- 

 ing to the seasons and the days. These tables, because 

 of their convenience, remained long in use. 



The work thus accomplished is worthy of admiration, 

 although Ptolemy lays himself open to the reproach 

 of not having passed on to us any accurate observations, 

 perhaps even of having made fictitious observations to 

 justify his hypotheses. 1 



The Tetrabiblos is a compendium of astrology, which 

 was wrongly, for a long time, not attributed to Ptolemy, 

 being considered unworthy of him. It gives a sys- 

 tematic outline of astrological questions and contains 

 many interesting ideas on the psychology of nations ; 

 it is far superior to similar works of that period. 

 Amongst these must be mentioned the dialogue 

 Hermippus, in which an unknown author defines the 

 position of Christianity in relation to astrology. 



Finally, in a geographical work, Ptolemy solves, 

 with much skill, the problem of the projection of a 

 spherical surface on a plane. 



In the realm of mathematics Menelaus published, 

 towards the end of the first century a.d., a writing 

 entitled On Spherics, which contains an important 

 theorem on the spherical triangle. Nicomachus of 

 Gerasa (Syria) brought out at almost the same time 

 (a.d. 150) an Introduction to Arithmetic, which was, as 

 we have seen, translated into Latin by Boetius. This 

 introduction, amongst other propositions, enunciates 

 the following : the cubes of whole numbers are 

 successively obtained by the addition of odd numbers 

 in this manner : 



3 + 5 = 2 3 , 7 + 9 + n = 3 3 , 13 + 15 + 17 + 19 = 4 3 > 

 21 + 23 + 25 + 27 + 29 = 5 3 , etc. 



As to Theon of Smyrna, he is chiefly known by an 

 1 2 Bigourdan, Astronomie, p. 295. 



