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( Archytas)
Archytas (Greek ????ta?; 428 BC – 347 BC) was an Ancient Greek philosopher, mathematician, astronomer, statesman, and strategist. He was a scientist of the Pythagorean school and famous for being the reputed founder of mathematical mechanics, as well as a good friend of Plato. Archytas was born in Tarentum, Magna Graecia (now Italy) and was the son of Mnesagoras or Histiaeus. For a while, he was taught by Philolaus, and was a teacher of mathematics to Eudoxus of Cnidus. Archytas and Eudoxus' student was Menaechmus. Archytas is believed to be the founder of mathematical mechanics.[1] As only described in the writings of Aulus Gellius five centuries after him, he was reputed to have designed and built the first artificial, self-propelled flying device, a bird-shaped model propelled by a jet of what was probably steam, said to have actually flown some 200 meters.[2][3] This machine, which its inventor called The Pigeon, may have been suspended on a wire or pivot for its flight.[4][5] Archytas also wrote some lost works, as he was included by Vitruvius in the list of the twelve authors of works of mechanics.[6] Thomas Winter has suggested that the pseudo-Aristotelian Mechanical Problems is an important mechanical work by Archytas, not lost after all, but misattributed.[7] According to Eutocius, Archytas solved the problem of doubling the cube in his manner with a geometric construction.[8] Hippocrates of Chios before, reduced this problem to finding mean proportionals. Archytas' theory of proportions is treated in book VIII of Euclid's Elements, where is the construction for two proportional means, equivalent to the extraction of the cube root. According to Diogenes Laertius, this demonstration, which uses lines generated by moving figures to construct the two proportionals between magnitudes, was the first in which geometry was studied with concepts of mechanics.[9] The Archytas curve, which he used in his solution of the doubling the cube problem, is named after him.
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