Archytas | |
|---|---|
 Bust fromVilla of the Papyri,Herculaneum, once identified as Archytas, now thought to bePythagoras[1] | |
| Born | 435/410 BC |
| Died | 360/350 BC |
| Philosophical work | |
| Era | Classical Greek philosophy |
| Region | Western philosophy |
| School | Pythagoreanism |
| Notable ideas | Doubling the cube Infinite universe |
Archytas (/ˈɑːrkɪtəs/;Greek:Ἀρχύτας; 435/410–360/350 BC[2]) was anAncient Greekmathematician,music theorist,[3] statesman, and strategist from the ancient city ofTaras (Tarentum) inSouthern Italy. He was a scientist and philosopher affiliated with thePythagorean school and famous for being the reputed founder of mathematical mechanics and a friend ofPlato.[4]
As a Pythagorean, Archytas believed that arithmetic (logistic), rather than geometry, provided the basis for satisfactory proofs,[5] and developed the most famous argument for the infinity of the universe in antiquity.[6]
Archytas was born in Tarentum, a Greek city in theItalian Peninsula that was part ofMagna Graecia, and was the son of Hestiaeus. He was presumably taught byPhilolaus, and taught mathematics toEudoxus of Cnidus and to Eudoxus' student,Menaechmus.[6]
Politically and militarily, Archytas appears to have been the dominant figure in Tarentum in his generation, somewhat comparable toPericles inAthens a half-century earlier.[7] The Tarentines elected himstrategos ("general") seven years in a row, a step that required them to violate their own rule against successive appointments. Archytas was allegedly undefeated as a general in Tarentine campaigns against their southern Italian neighbors.[8]
In his public career, Archytas had a reputation for virtue as well as efficacy. TheSeventh Letter, traditionally attributed toPlato, asserts that Archytas attempted to rescue Plato during his difficulties withDionysius II ofSyracuse.[9] Some scholars have argued that Archytas may have served as one model for Plato'sphilosopher king, and that he influenced Plato's political philosophy as expressed inThe Republic and other works.[6]
Archytas is said to be the first ancient Greek to have spoken of the sciences ofarithmetic (logistic),geometry,astronomy, andharmonics as kin, which later became the medievalquadrivium.[10][11] He is thought to have written a great number of works in the sciences, but only four fragments are generally believed to be authentic.[12]
According toEutocius, Archytas was the first to solve the problem ofdoubling the cube (the so-calledDelian problem) with an ingenious geometric construction.[13][14] Before this,Hippocrates of Chios had reduced this problem to the finding of two meanproportionals, equivalent to the extraction ofcube roots. Archytas' demonstration uses lines generated by moving figures to construct the two proportionals between magnitudes and was, according toDiogenes Laërtius, the first in which mechanical motions entered geometry.[a] The topic of proportions, which Archytas seems to have worked on extensively, is treated inEuclid'sElements, where the construction for two proportional means can also be found.[16]
Archytas named theharmonic mean, important much later inprojective geometry andnumber theory, though he did not discover it.[17] He proved thatsupernummerary ratios[b] cannot be divided by a mean proportional – an important result in ancient harmonics.[6]Ptolemy considered Archytas the most sophisticated Pythagorean music theorist, and scholars believe Archytas gave a mathematical account of the musical scales used by practicing musicians of his day.[18]
Later tradition regarded Archytas as the founder of mathematicalmechanics.[19]Vitruvius includes him in a list of twelve authors who wrote works on mechanics.[20] T.N. Winter presents evidence that the pseudo-AristotelianMechanical Problems might have been authored by Archytas and later mis-attributed toAristotle.[21] Tradition also has it that Archytas built a mechanical flying dove. The sole mention of this from antiquity comes some five centuries after Archytas, whenAulus Gellius discusses a report by his mentorFavorinus:[22][23]
Archytas made a wooden model of a dove with such mechanical ingenuity and art that it flew; so nicely balanced was it, you see, with weights and moved by a current of air enclosed and hidden within it. About so improbable a story I prefer to give Favorinus' own words: "Archytas the Tarentine, being in other lines also a mechanician, made a flying dove out of wood. Whenever it lit, it did not rise again."
Aulus Gellius views the reporting of the tradition as problematic, since it spreads implausible beliefs even if accompanied by skepticism.[24][25]
Laërtius, Diogenes."Pythagoreans: Archytas" .Lives of the Eminent Philosophers. Vol. 2:8. Translated byHicks, Robert Drew (Two volume ed.). Loeb Classical Library.:Vitae philosophorum
