ON THE HISTORY OF MECHANICS. 239 



Archytasof Tarentum, and Eiicloxus of Cnidus were also Pythagoreans. They 

 were the first that attempted to make the mathematical sciences familiar by 

 popular illustrations; and Archytas is said by some to have invented the pul- 

 ley and the screw. They lived nearly 150 years after Pythagoras, and geo- 

 metry had made in the mean time very rapid advances, for the properties of 

 the conic sections were well known to these philosophers. " The first per- 

 sons," 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 solu- 

 tions of problems, which, if more mathematically treated, are complicated 

 and difficult: each of them invented a method of determining in this manner 

 the magnitude of two mean proportionals between two given lines, by the as- 

 sistance of certain curves and sections. Plato by no means approved of their 

 mode of proceeding, and reprehended them severely, as giving up and pervert- 

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

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

 subjected 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 lulf a century after Archytas; he was perhaps the author of no ori- 

 ginal 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. Dino- 

 crates 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 



