ARCHYTAS of Tarentum was a Pythagorean philosopher, well skilled in mathematics and geography. He lived in the time of Plato, and, according to report, interposed his influence with Dionysius the tyrant, in order to save the life of that philosopher. According to this date, it would appear that Jamblichus is mistaken when he asserts that he was a hearer of Pythagoras; and the testimony of a writer mentioned by Photius would seem more worthy of credit, that he was the eighth successive preceptor of the Pythagorean school. So eminent were his military talents, that, in opposition to an express law of his country, that no man should be chosen more than once the general of its armies, he was elevated to that station no less than seven times. He taught that there is nothing so destructive to man as pleasure; that virtue is to be pursued for its own merit, and that every extreme is incompatible with it. Aristotle, according to some, was indebted to Archytas for his general heads of arrangement entitled his Ten Categories. By discovering the duplication of the cube by means of the conic sections, and the method of finding two mean proportions between two given lines, he displayed his great knowledge in mathematics. Archytas is reported to have invented several curious hydraulic machines, and his genius is likewise honoured with the invention of the screw and crane. He perished in a shipwreck, and his body was found on the Apulian coast—an occurrence commemorated in one of Horace's Odes. A treatise on the Categories, bearing his name, was published by J. Camerarius at Leipzig, in 8vo, in 1564. Certain Fragments, also ascribed to him, were published by J. Gramm at Copenhagen, in 4to, in 1707.