120 



Pythagoras himself discovered the 47th proposition of Euclid, 

 or met with it in Iris travels ; it is, however, cpiite certain that 

 the transcendent genius of Plato — one of the foremost, perhaps 

 the very foremost, in the rank of human intelligences — was 

 the first who systematized and reduced into logical order 

 the mathematical knowledge then floating in the minds of his 

 contemporaries. Not only did he do this, but he conceived 

 and investigated the properties of these lines, which the 

 scarcely less illustrious genius of a later age demonstrated to 

 be the courses of the planets. It is hardly necessary to say 

 that I allude to the curves known as the conic sections. It 

 is an observation constantly obtruded on us by the utilitarian 

 tendencies of the time we live in, that abstract speculations 

 are useless, that they occupy time which might better be de- 

 voted to objects of greater utility, and all the other trite 

 truisms of an age material in its conceptions and its pursuits. 

 Yet, had Plato and his followers been deterred by considera- 

 tions of this kind from their geometrical investigations, the 

 properties of the conic sections had remained unknown. 

 Kepler, when he failed in adjusting the motions of Mars to 

 a circrdar orbit, had never thought of the ellipse ; Newton 

 had failed to discover the law of attraction, and thus the 

 theory of universal gravitation — the proudest monument of 

 human genius — would still have lain far beyond the confines 

 of human knowledge. 



" This is not the place to discuss or inquire into the history 

 of those discoveries, which the unanimous voice of an admiring 

 posterity has, with one accord, attributed to the geometers of 

 Greece. The names of Euclid, of Plato, of Archimedes, and 

 Apollonius of Perga, are amongst us as household words. On 

 the subjugation of that highly favoured people to a foreign 

 power (and the same phenomenon was witnessed, almost iden- 

 tical in its phases, many ages later among the free states and 

 busy republics of mediccval Italy), science fled the land ; 

 while art no longer elevated the conceptions or refined the 



