ARCHYTAS, a Pythagorean philosopher, and the friend and contemporary of Plato, was the son of Hes timus of Tarentum, and flourished about 400 years be fore Christ. When his master Plato was threatened with death by the tyrant Dionysius of Sicily, he gene rously interposed, and saved his life. In opposition to an established law, which provided that no person should hold more than once the command of the army, Archy tas was seven times called by his countrymen to that high office, and he was as frequently chosen the chief magistrate of Tarentum. Archytas was one of the most distinguished mathematicians of the Platonic school.
The celebrated problem of the duplication of the cube had long perplexed the Greek geometers. Hippocrates discovered, that, if two mean proportionals between the side of the given cube and its double, could be found, the first of them would be the side of the cube sought. Plato had given a practical solution of this problem Ar chytas imagined a curve, described by a particular mo tion on the surface of a cylinder, and which, being met by the surface of a cone situated in a particular manner, gave one of the mean proportionals ; but this was a so lution more curious than useful. Archytas is said to have
invented the screw, the crane, and several hydraulic ma chines ; but on these subjects no certain information has been transmitted to the present day. It appears, from the following passage in Horace, that Archytas was ship wrecked on the coast of Apulia :— Te Maris et terra, numerocpie carentis arena Mensorem cohibent, Archyta.
Pulveris exigui prope littus parva Matinum Munera nee quidquatn tibi prodest Aerias tentasse domos, animogne rotundum Pereurrisse polum morituro.
A metaphysical work of Archytas's, entitled, fleet ra moon; PioEwe, "On the Universe," is still extant. See Fabric. Bib!. GMYC. lib. ii. cap. 13. Diog. in Vit. Cic. 3. de Orat. Brucker's Hist. Phil. by Enfield, vol. i. p. 410. Montucla's Hist. des Math. torn. i. p. 188. 196. (70