60 GREEK GEOMETRY. 



called synthesis, or composition, in opposition to the analysis, or 

 the process of investigation : and it is frequently said that 

 Plato imported the whole system in the visits which he 

 made like Thales of Miletus and Pythagoras, to study under 

 the Egyptian 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 

 geometers had worked their problems and theorems at 

 random ; that Thales and Pythagoras with their disciples, a 

 century and a half before Plato, and Hippocrates, 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 improved and further systematised the method, as he 

 was no doubt deeply impressed with the paramount import- 

 ance 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 exaggeration 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 pro- 

 bability. 



Of the works written by the Greek geometers some have 

 come down to us ; some of the most valuable, as the ' Ele- 

 ments ' 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 century, has left a valuable account of 

 the geometrical writings of the elder Greeks. His work is 

 of a miscellaneous nature, as its name, ' Mathematical Collec- 

 tions,' implies ; and excepting a few passages, it has never 

 been published in the original Greek. Commandini, of Ur- 

 bino, made a translation of the whole six books then dis- 

 covered ; the first has never been found, but half the second 

 being in the Savilian library at Oxford, was translated by 

 Wallis a centuiy later. Commandini's translation, with his 

 learned commentary, was not printed before his death, but 



