THE GRECO-ROMAN PERIOD 99 



with geometrical tradition, he still calls a square the 

 product of two numbers ; his method, on the contrary, 

 is purely arithmetical. The problems are treated with 

 much elegance, but point by point, without bringing in 

 any general formulae. The result is that Diophantus 

 rejects as impossible the negative or irrational roots of 

 an equation, and that, where two positive roots are 

 possible he only keeps one. The problems set are 

 very varied and lead to equations of the first, second, 

 and sometimes third degree with one or more variables. 

 One of these problems relates to the price of wine, and 

 it is by the data of this problem that P. Tannery has 

 fixed the period in which Diophantus lived. 1 



An interesting fact to be noted in the history of the 

 mathematics of this period is the lively interest taken 

 in them by the Neo-platonic school of philosophy. 

 Porphyry and Iamblichus devoted several writings 

 to arithmetical questions, and Proclus in the fifth 

 century a.d. wrote an interesting commentary on the 

 works of Plato and the first book of Euclid. 



Amongst other commentators of the period we must 

 point out Simplicius, who, in 529 a.d., after the closing 

 of the university of Athens by Justinian, fled into 

 Persia, and whose commentaries on Aristotle are 

 invaluable ; also Eutocius of Ascalon, to whom we owe 

 an edition of the Conic Sections of Apollonius, and of 

 some writings of Archimedes with explanatory notes. 

 His work was rescued from oblivion by Isidore of 

 Miletus, the architect of St. Sophia. 



It was likewise to such commentaries that the later 

 representatives of the mathematical school of Alexan- 

 dria devoted their energies. Theon, about the year 

 370 a.d., edited the Elements of Euclid and the short 

 course of astronomy which had been extracted from 

 the Almagest for the purpose of teaching. His 

 daughter Hypatia, who fell a victim to the fanaticism 

 1 28 Tannery, Memoires scientifiques, p. 70. 



