138 A SHORT HISTORY OF SCIENCE 



his peer in Apollonius. . . . His work is only the last convulsive effort 

 of Greek geometry, which was now nearly dead, and was never effec- 

 tually revived. ... It is not so with Ptolemy or Diophantus. The 

 trigonometry of the former is the foundation of a new study which was 

 handed on to other nations, indeed, but which has thenceforth a con- 

 tinuous history of progress. Diophantus also represents the outbreak 

 of a movement which probably was not Greek in its origin, and which 

 the Greek genius long resisted, but which was especially adapted to 

 the tastes of the people who, after the extinction of Greek schools, 

 received their heritage and kept their memory green. But no Indian 

 or Arab ever studied Pappus or cared in the least for his style or his 

 matter. When geometry came once more up to his level, the inven- 

 tion of analytical methods gave it a sudden push which sent it far 

 beyond him and he was out of date at the very moment when he seemed 

 to be taking a new lease of life. 



A melancholy interest attaches to the fate of Hypatia, daughter 

 of Theon an Alexandrian mathematician, herself a teacher of 

 Greek philosophy and mathematics, who was torn to pieces by 

 a Christian mob, doubtless as a representative of pagan (Greek) 

 learning, at Alexandria in 415 A.D. 



CONCLUSION AND RETROSPECT. - - Intellectual interests in the 

 Greek world (now really Roman) were by this time so completely 

 alienated from mathematics, and indeed from science in general, 

 that the brilliant work of Pappus and Diophantus aroused but 

 slight and temporary interest. Geometry had reached within the 

 possible range of the Euclidean method a relatively complete 

 development. Algebra under Diophantus attained in spite of 

 hampering notation a level not again approached for many cen- 

 turies. 



Little need be said of sciences other than those already dealt 

 with. These, even more than mathematics and astronomy, shrank 

 under Roman autocracy and Christian hostility. Only the 

 works of Galen, Strabo, and Pliny need be mentioned, and with 

 them we deal in the next chapter. 



The torch of science now passes from the Greeks to the Indians 

 of the far East after their conquest by Alexander, to be in turn 



