SIMSON. 471 



geometers, and afterwards to converse with Theodoras 

 at Gyrene, and the Pythagorean School in Italy. But 

 it can hardly be supposed that all the preceding geo- 

 meters had worked their problems and theorems at 

 random ; that Thales and Pythagoras with their dis- 

 ciples, a century and a half before Plato, and Hip- 

 pocrates, half a century before his time, had no 

 knowledge of the analytical method, and pursued no 

 systematic plan in their researches, devoted as their 

 age was to geometrical studies. Plato may have im- 

 proved and further systematized the method, as he was 

 no doubt deeply impressed with the paramount im- 

 portance of geometry, and even inscribed upon the gates 

 of the Lyceum a prohibition against any one entering 

 who was ignorant of it. The same spirit of exaggera- 

 tion which ascribes to him the analytical method, has 

 also given rise to the notion that he was the discoverer 

 of the Conic Sections ; a notion- which is without any 

 truth and without the least probability. 



Of the works written by the Greek geometers some 

 have come down to us ; some of the most valuable, as 

 the ' Elements' and ' Data' of Euclid, and the ' Conies' 

 of Apollonius. Others are lost ; but, happily, Pappus, 

 a mathematician of some merit, who flourished in the 

 Alexandrian school about the end of the fourth cen- 

 tury, has left a valuable account of the geometrical 

 writings of the elder Greeks. His work is of a mis- 

 cellaneous nature, as its name, 'Mathematical Col- 

 lections,' implies ; and excepting a few passages, it has 

 never been published in the original Greek. Com- 

 mandini, of Urbino, made a translation of the whole 

 six books then discovered; the first has never been 



