ON THE HISTORY OF MECHANICS.

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Archytasof Tarentum,and Eudoxus of Cnidus were also Pythagoreans . TheyWe re the first that attempted to make the mathematical sciences familiar bypopular 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 ofthe conic sections were well known to these philosophers. “ Hie first per-sons,” says Plutarch , “that cultivated the,method of organic geometry, were ofthe school of Eudoxus and Archytas . These philosophers introduced eleganceand variety into science, by illustrations derived from sensible objects, andmade use of mechanical contrivances for expediting and familiarising the solurtions of problems, which, if more mathematically treated, are complicatedand difficult: each of them invented a method of determining in this mannerthe magnitude of two mean proportionals between two given lines,by the as-sistance of certain curves and sections. Plato by no means approved of theirmode of proceeding,and reprehended them severely,as giving up and pervert-ing the most essential advantages ot geometry, and causing the science tor evert from pure and incorporeal forms to the qualities of sensible bodies,Subjected to narrow anil servile restraints. It was tor this reason that practi-cal mechanics were separated from geometry, and were long neglected byPhilosophers , being considered as a department only of.the art of war.”

Aristotle , who was almost the last of the Ionian school, flourished a little^ ess than half a century after Archytas ; he was perhaps the author of no ori-Smal discoveries relating to the principles of mechanics, but we find, in his| r eati se on this science, the law of the composition of motion very distinctly^ a, d down; he makes, however, some mistakes respecting the properties ofv ers. His general merit in elegant literature, as well as in natural history4u d natural philosophy", is too well known to require encomium.

. The foundation of Alexandria commences a period memorable for scienceln general, hut more particularly for mathematics and astronomy. l)ino-cra tes was the architect whom Alexander employed in laying out and mbuilding this celebrated city. Among those who studied in this school, thefences are indebted to none more than to Euclid, who lived about 300years before our era. It is uncertain how much of his Elements may have^ ee u derived from his own investigations; but the masterly' mannei in which