242 LECTURE XX. 



being rivalled by the accuracy and vigour of the other. It is impossible that 

 propositions more difficult and important should be deduced from simpler and 

 purer elements. Some attribute this excellence to his natural genius, others to 

 his indefatigable application, which has given to every thing that he has 

 attempted the appearance of having been performed'wlth ease. For we might 

 ourselves search in vain for a demonstration of his propositions; but so smooth 

 and direct is the way by which he leads us, that when we have once passed 

 it, we fancy that we could readily have found it without assistance. We may, 

 therefore, easily give credit to what is said of him, that being as it were fas- 

 cinated by this domestic syren, that bore him company, he often neglected his 

 food and his clothing; that when sometimes brought by compulsion to the 

 baths, he used to draw his figures in the ashes of the fire places, and to make 

 his calculations upon the cosmetics that were employed by the attendants; de- 

 riving, like a true votary of the muses, every pleasure from an intellectual 

 origin. Among all his beautiful discoveries, he is said to have chosen that 

 of the proportion of the sphere and cylinder for his sepulchral honours; re- 

 questing of his friends that they would place on his tomb a cylinder contain- 

 ing a sphere, and inscribe on it the ratio which he had first determined. 



" By artifice, and through the thoughtlessness and security of a day of 

 festivity, the Romans at length obtained possession of Syracuse, and in the 

 pillage, although orders had been issued that the life of Archimedes should 

 be spared, he was killed by a private soldier. His death is variously related, 

 but all accounts agree, that Marcellus was deeply concerned for his loss, that 

 he held his assassin in abhorrence, and conferred distinguished favours on his 

 surviving relations." This event is supposed to have happened about 212 

 years before the birth of Christ: and the cultivation of mechanical philosophy, 

 which had been continued for four hundred years with increasing success, was 

 almost wholly interrupted for eighteen centuries. 



There lived, however, in the mean time, some mathematicians and mechanics 

 of considerable merit. A work on warlike machines, addressed to Marcellus 

 by Athenaeus, is still extant, and may be found in the splendid collection 

 of writers on military mechanics entitled Mathematicl Veteres. Ctesibius of 

 Alexandria was about a century later than Archimedes; he enriched hydrau- 

 lics with several valuable machines; although he contributed little to the ad- 



