Archytas

Template:Short description {{#invoke:other uses|otheruses}} Template:Infobox philosopher

Archytas (Template:IPAc-en; Template:Langx; 435/410–360/350 BC<ref>Philippa Lang, Science: Antiquity and its Legacy, Bloomsbury Academic, 2015, p. 154.</ref>) was an Ancient Greek mathematician, music theorist,<ref>Template:Cite encyclopedia Template:Grove Music subscription</ref> statesman, and strategist from the ancient city of Taras (Tarentum) in Southern Italy. He was a scientist and philosopher affiliated with the Pythagorean school and famous for being the reputed founder of mathematical mechanics and a friend of Plato.<ref>Debra Nails, The People of Plato, Template:ISBN, p. 44</ref>

As a Pythagorean, Archytas believed that arithmetic (logistic), rather than geometry, provided the basis for satisfactory proofs,<ref>Morris Kline, Mathematical Thought from Ancient to Modern Times Oxford University Press, 1972 p. 49</ref> and developed the most famous argument for the infinity of the universe in antiquity.<ref name=":0">Template:Citation</ref>

Life

Archytas was born in Tarentum, a Greek city in the Italian Peninsula that was part of Magna Graecia, and was the son of Hestiaeus. He was presumably taught by Philolaus, and taught mathematics to Eudoxus of Cnidus and to Eudoxus' student, Menaechmus.<ref name=":0" />

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.<ref>Template:Cite journal</ref> The Tarentines elected him strategos ("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.<ref>{{#invoke:citation/CS1|citation |CitationClass=web }}</ref>

In his public career, Archytas had a reputation for virtue as well as efficacy. The Seventh Letter, traditionally attributed to Plato, asserts that Archytas attempted to rescue Plato during his difficulties with Dionysius II of Syracuse.<ref>Template:Cite journal</ref> 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.<ref name=":0" />

Works

Archytas is said to be the first ancient Greek to have spoken of the sciences of arithmetic (logistic), geometry, astronomy, and harmonics as kin, which later became the medieval quadrivium.<ref> Template:Cite journal </ref><ref> Template:Cite book </ref> He is thought to have written a great number of works in the sciences, but only four fragments are generally believed to be authentic.<ref> Template:Cite book </ref>

According to Eutocius, Archytas was the first to solve the problem of doubling the cube (the so-called Delian problem) with an ingenious geometric construction.<ref> Template:Cite book </ref><ref> Template:Cite journal </ref> Before this, Hippocrates of Chios had reduced this problem to the finding of two mean proportionals, equivalent to the extraction of cube roots. Archytas' demonstration uses lines generated by moving figures to construct the two proportionals between magnitudes and was, according to Diogenes Laërtius, the first in which mechanical motions entered geometry.Template:Efn The topic of proportions, which Archytas seems to have worked on extensively, is treated in Euclid's Elements, where the construction for two proportional means can also be found.<ref> Template:Cite book </ref>

Archytas named the harmonic mean, important much later in projective geometry and number theory, though he did not discover it.<ref> Template:Cite report </ref> He proved that supernummerary ratiosTemplate:Efn cannot be divided by a mean proportional – an important result in ancient harmonics.<ref name=":0"/> 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.<ref> Template:Cite journal </ref>

File:The flying pigeon of Archytas, Kotsanas Museum of Ancient Greek Technology.jpg

A reconstruction of Archytas' flying dove (5th c. B.C.), in Kotsanas Museum of Ancient Greek Technology, Athens, Greece.

Later tradition regarded Archytas as the founder of mathematical mechanics.<ref name="Diogenes Laërtius"> Template:Cite LotEP: Vitae philosophorum </ref> Vitruvius includes him in a list of twelve authors who wrote works on mechanics.<ref> Template:Cite book </ref> T.N. Winter presents evidence that the pseudo-Aristotelian Mechanical Problems might have been authored by Archytas and later mis-attributed to Aristotle.<ref> Template:Cite report </ref> Tradition also has it that Archytas built a mechanical flying dove. The sole mention of this from antiquity comes some five centuries after Archytas, when Aulus Gellius discusses a report by his mentor Favorinus:<ref> Template:Cite conference </ref><ref> Template:Cite book </ref>

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."{{#if:|{{#if:|}}

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Aulus Gellius views the reporting of the tradition as problematic, since it spreads implausible beliefs even if accompanied by skepticism.<ref> Template:Cite book</ref><ref>Template:Cite journal</ref>

Further reading

• Template:Cite encyclopedia on line [1]
• Huffman, Carl A. Archytas of Tarentum, Cambridge University Press, 2005, Template:ISBN

External links

• Template:Cite SEP
• Template:MacTutor Biography
• Pseudo-Aristotle, Mechanica – Greek text and English translation
• Complete fragments (Greek–Spanish bilingual edition)
• Fragments and Life of Archytas