DEVELOPMENT OF MATHEMATICAL THOUGHT. 633 



and the well-known references to mathematical ideas 

 in the schools of Pythagoras and Plato indicate. An 

 ancient fragment 1 which enumerates briefly the Grecian 

 mathematicians, says of Pythagoras, " He changed the oc- 

 cupation with this branch of knowledge into a real science, 

 inasmuch as he contemplated its foundation from a 

 higher point of view, and investigated the theorems 

 less materially and more intellectually ; " 2 and of Plato 

 it says that " He filled his writings with mathematical 

 discussions, showing everywhere how much of geometry 

 attaches itself to philosophy." 3 



This twofold connection of mathematical with other 

 pursuits has, after the lapse of many centuries, come 

 prominently forward again in the nineteenth century. 

 We have already had to record a powerful stimulus to 

 mathematical thought in almost every chapter in which 

 we dealt with the fruitful ideas which governed scientific 

 work, and we have now no less to draw attention to the 

 philosophical treatment which has been bestowed upon 

 the foundations of science and the inroad of mathemati- 



changes radically. Whilst among 

 the earlier civilised nations we only 

 meet with routine and practice, 

 with empirical rules which served 

 practical purposes in an isolated 

 manner, the Grecian mind on the 

 other side recognised, from the 

 first moment when it became 

 acquainted with this matter, that 

 it contained something which tran- 

 scended all those practical ends, 

 but which was worthy of special 

 attention, and which could be ex- 

 pressed in a general form, be- 

 ing, in fact, an object of science. 

 This is the high merit of the Greek 

 mathematicians ; nor need one fear 



that this merit should be dimin- 

 ished by admitting that they bor- 

 rowed the new material from the 

 ancient Egyptian civilisation." 



1 The fragment referred to is 

 preserved by Proclus. and is given 

 in full in Cantor's work (vol. i. p. 

 124 sqq.) He calls it an ancient 

 catalogue of mathematicians. It 

 is generally attributed to Eudemus 

 of Rhodes, who belonged to the 

 peripatetic school of philosophy, 

 and was the author of several his- 

 torical treatises on geometry and 

 astronomy (Cantor, vol. i. p. 108). 



2 Cantor, vol. i. p. 137. 



3 Ibid., p. 213. 



