3.40 LECTUUE XX. 



this well known work is arranged, and the precision and accuracy which reign 

 in every part of it, demand ahnost as great a share of praise as is due to ori- 

 ginal discovery. 



Epicurus was a cotemporary of Euclid, and is considered as the last of the 

 Pythagorean or Italian philosophers. The penetration that he discovered in 

 assigning the true causes to many mechanical phenomena, his explanations of 

 which are copied by Lucretius, is sufficient to induce us to look forwards 

 with impatience to the publication of such of his works, as have lately been 

 discovered amongthe manuscripts of Ilerculaneum. Apollonius of Perga lived 

 about half a century later ; the elegance and extent of his investigations of 

 the most abstruse properties of the conic sections left but little to be added 

 to them by more modern geometricians. The architect Philo appears to have 

 been more ancient than Apollonius: but he is not the Philo whose essay on 

 warHke engines is published in the collection of the Ancient mathematicians; 

 since this author was a pupil of Ctesibius. 



For the demonstration of the fundamental properties of the lever and of 

 the centre of gravity; for the discovery of the laws of h3'drostatics, and of the 

 modes of determining the specific gravities of bodies; for the construction of 

 the first cranes, and of the first planetarium; and for those improvements of 

 the methods of mathematical investigation which have been the basis of every 

 modern refinement in analytical calculation; for all these additions to our 

 knowledge and our powers, we are indebted to Archimedes. On a character 

 so conspicuous, we can with pleasure dwell long enough to attend to some 

 particulars of his history, which are related by Plutarch, in his account of the 

 siege of Syracuse; omitting, however, such details as are evidently 

 fabulous. " Archimedes," says Plutarch, " armed with his own inven- 

 tions only, made light of the splendour of the Roman preparations, and of 

 the glory of the name of Marcellus. And these were inventions that he even 

 considered as of subordinate value, as geometrical playthings, which had been 

 the amusements of his leisure hours. It was king Hiero that first induced 

 him to transfer a portion of his science from intellectual to materinl objects, 

 and to condescend in some degree to the comprehension of the multitude, by 

 giving a sensible form to those truths, which in their abstract state are disco- 

 verable only to the reasoning faculty. Archimedes, who was a friend and a 



