ON THE HISTORY OF MECHANICS. 183 



for the properties of the conic sections were well known to these philoso- 

 phers. " The first persons," says Plutarch, " that cultivated the method 

 of organic geometry, were of the school of Eudoxus and Archytas. These 

 philosophers introduced elegance and variety into science, by illustrations 

 derived from sensible objects, and made use of mechanical contrivances for 

 expediting and familiarising the solutions of problems, which, if more 

 mathematically treated, are complicated and difficult : each of them in- 

 vented a method of determining in this manner the magnitude of two 

 mean proportionals between two given lines, by the assistance of certain 

 curves and sections. Plato by no means approved of their mode of pro- 

 ceeding, and reprehended them severely, as giving up and perverting the 

 most essential advantages of geometry, and causing the science to revert 

 from pure and incorporeal forms to the qualities of sensible bodies, sub- 

 jected to narrow and servile restraints. It was for this reason that practi- 

 cal mechanics were separated from geometry, and were long neglected by 

 philosophers, being considered as a department only of the art of war." 



Aristotle, who was almost the last of the Ionian school, flourished a 

 little less than half a century after Archytas ; he was perhaps the author 

 of no original discoveries relating to the principles of mechanics, but we 

 find, in his treatise on this science, the law of the composition of motion 

 very distinctly laid down ; he makes, however, some mistakes respecting 

 the properties of levers. His general merit in elegant literature, as well as 

 in natural history and natural philosophy, is too well known to require 

 encomium. 



The foundation of Alexandria commences a period memorable for 

 science in general, but more particularly for mathematics and astronomy. 

 Dinocrates was the architect whom Alexander employed in laying out and 

 in building this celebrated city. Among those who studied in this school, 

 the sciences are indebted to none more than to Euclid, who lived about 300 

 years before our era. It is uncertain how much of his Elements may 

 have been derived from his own investigations ; but the masterly manner 

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

 which reign in every part of it, demand almost as great a share of praise 

 as is due to original discovery. 



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

 the Pythagorean or Italian philosophers. The penetration that he dis- 

 covered 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 among the manuscripts of Herculaneum. 

 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 warlike 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 



