Archytas

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Western Philosophy Pre-Socratic philosophy
Archytas
Name:	Archytas
Birth:	428 BC
Death:	347 BC
School/tradition:	Pythagoreanism
Main interests:	-
Notable ideas:	-
Influences:	Philolaus
Influenced:	Menaechmus

Archytas (Greek: Αρχύτας; 428 BC-347 BC) was an Ancient Greek philosopher, mathematician, astronomer, statesman, and strategist.

Archytas was born in Tarentum, Magna Graecia (now Italy) and was the son of Mnesagoras or Histiaeus. He was taught for a while by Philolaus and he was a teacher of mathematics to Eudoxus of Cnidus. He was a scientist of the Pythagorean school and famous for being a good friend of Plato. His and Eudoxus' student was Menaechmus.

Archytas

Archytas is believed to be the founder of mathematical mechanics.^[1] He is 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 yards.^[2] This machine, which its inventor called The Pigeon, may have been suspended on a wire or pivot for its flight.^{[citation needed]} Archytas also wrote some lost works, as he was included by Vitruvius in the list of the twelve authors of works of mechanics.^[3]

According to Eutocius, Archytas solved the problem of doubling the cube in his manner with a geometric construction.^[4] Hippocrates of Chios before, reduced this problem to finding mean proportionals. Archytas' theory of proportions is treated in the 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.^[5] The Archytas curve, which he used in his solution of the doubling the cube problem, is named after him.

Politically and militarily, Archytas appears to have been the dominant figure in Tarentum in his generation, somewhat comparable to Pericles in Athens a half-century earlier. The Tarentine elected him strategos, "general", seven years in a row — a step that required them to violate their own rule against successive appointments. He was allegedly undefeated as a general, in Tarentese campaigns against their southern Italian neighbors. The Seventh Letter of Plato asserts that Archytas attempted to rescue Plato during his difficulties with Dionysius II of Syracuse. In his public career, Archytas had a reputation for virtue as well as efficacy. Some scholars have argued that Archytas may have served as one model for Plato's philosopher king, and that he influenced Plato's political philosophy as expressed in The Republic and other works (i.e., how does a society obtain good rulers like Archytas, instead of bad ones like Dionysus II?).

Archytas was drowned in the Adriatic Sea; his body lay unburied on the shore till a sailor humanely cast a handful of sand on it, otherwise he would have had to wander on this side the Styx for a hundred years, such the virtue of a little dust, munera pulveris, as Horace calls it.

The Archytas crater on the Moon was named in his honour.

[edit] Notes

^ Diogenes Laertius, Vitae philosophorum, viii.83.
^ Aulus Gellius [1]
^ Vitruvius, De architectura, vii.14.
^ Eutocius, commentary on Archimedes' On the sphere and cylinder.
^ Plato blamed Archytas for his contamination of geometry with mechanics (Plutarch, Questionum convivialium libri iii, 718E-F): And therefore Plato himself dislikes Eudoxus, Archytas, and Menaechmus for endeavoring to bring down the doubling the cube to mechanical operations; for by this means all that was good in geometry would be lost and corrupted, it falling back again to sensible things, and not rising upward and considering immaterial and immortal images, in which God being versed is always God.