76 SCIENCE IN GRECO-ROMAN ANTIQUITY 



of Jerusalem. In it new examples of the use of 

 infinitesimal mechanical integration are described and 

 worked out. 1 The Lemmas is perhaps an apocry- 

 phal work. As to the celebrated Cattle-Problem, it 

 was propounded by Archimedes in the form of an 

 epigram of forty-seven lines. It relates to the calcu- 

 lation of the number of oxen in a herd, being given 

 that they are penned in order according to a regular 

 figure, and that the animals of different colours occur 

 in proportions successively dependent on one another. 

 The work of Archimedes is so profound and original 

 that we heartily endorse the judgment of Leibnitz : 

 " He who understands Archimedes and Apollonius 

 finds less to admire in the inventions of the greatest 

 modern scientists." 



Apollonius of Perga (260-200 b.c.) is the third 

 great mathematician of this period. Pappus repre- 

 sents him as vain and always ready to depreciate the 

 worth of other geometers (Pappus, Hultsch edition, p. 

 678). In reality we do not know much about him, 

 except that he was surnamed Epsilon, probably because 

 the hall in which he gave his lectures bore the number 

 e = 5. He taught for several years in Alexandria, 

 then in the university of Pergamum which had just 

 been founded ; after which he returned to Alexandria, 

 where he remained until his death. 2 Of his masterly 

 work on Conic Sections we only possess the four first 

 books in the original Greek, the next three have been 

 preserved in an Arabic translation, but the eighth and 

 last is entirely lost. These books are dedicated partly 

 to Eudemus, partly to Attalus, who is supposed by 

 some to be Attalus I, King of Pergamum. In these 

 dedications, Apollonius specifies the relation of his own 



1 See the articles of Th. Reinach and P. Painleve in the 

 Revue generate des Sciences pures et appliquees, November 30 

 and December 15, 1907. 



2 23 Rouse Ball, History of Mathematics, p. 81. 



