Archytas (; el, Ἀρχύτας; 435/410–360/350 BC) was an

Ancient Greek Ancient Greek includes the forms of the Greek language used in ancient Greece and the ancient world from around 1500 BC to 300 BC. It is often roughly divided into the following periods: Mycenaean Greek (), Dark Ages (), the Archaic peri ...

philosopher A philosopher is a person who practices or investigates philosophy. The term ''philosopher'' comes from the grc, φιλόσοφος, , translit=philosophos, meaning 'lover of wisdom'. The coining of the term has been attributed to the Greek th ...

mathematician A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, structure, space, models, and change. History On ...

music theorist Music theory is the study of the practices and possibilities of music. ''The Oxford Companion to Music'' describes three interrelated uses of the term "music theory". The first is the "rudiments", that are needed to understand music notation (ke ...

astronomer An astronomer is a scientist in the field of astronomy who focuses their studies on a specific question or field outside the scope of Earth. They observe astronomical objects such as stars, planets, natural satellite, moons, comets and galaxy, g ...

statesman A statesman or stateswoman typically is a politician who has had a long and respected political career at the national or international level. Statesman or Statesmen may also refer to: Newspapers United States * ''The Statesman'' (Oregon), a n ...

, and

strategist A strategist is a person with responsibility for the formulation and implementation of a strategy. Strategy generally involves setting goals, determining actions to achieve the goals, and mobilizing resources to execute the actions. A strategy ...

. He was a scientist of the

Pythagorean Pythagorean, meaning of or pertaining to the ancient Ionian mathematician, philosopher, and music theorist Pythagoras, may refer to: Philosophy * Pythagoreanism, the esoteric and metaphysical beliefs purported to have been held by Pythagoras * Ne ...

school and famous for being the reputed founder of mathematical mechanics, as well as a good friend of

Plato Plato ( ; grc-gre, Πλάτων ; 428/427 or 424/423 – 348/347 BC) was a Greek philosopher born in Athens during the Classical period in Ancient Greece. He founded the Platonist school of thought and the Academy, the first institution ...

Life and work

Archytas was born in

Tarentum Tarentum may refer to: * Taranto, Apulia, Italy, on the site of the ancient Roman city of Tarentum (formerly the Greek colony of Taras) **See also History of Taranto * Tarentum (Campus Martius), also Terentum, an area in or on the edge of the Camp ...

Magna Graecia Magna Graecia (, ; , , grc, Μεγάλη Ἑλλάς, ', it, Magna Grecia) was the name given by the Romans to the coastal areas of Southern Italy in the present-day Italian regions of Calabria, Apulia, Basilicata, Campania and Sicily; these re ...

and was the son of Mnesagoras or Hadees. For a while, he was taught by

Philolaus Philolaus (; grc, Φιλόλαος, ''Philólaos''; ) was a Greek Pythagorean and pre-Socratic philosopher. He was born in a Greek colony in Italy and migrated to Greece. Philolaus has been called one of three most prominent figures in the Pytha ...

, and was a teacher of mathematics to

Eudoxus of Cnidus Eudoxus of Cnidus (; grc, Εὔδοξος ὁ Κνίδιος, ''Eúdoxos ho Knídios''; ) was an ancient Greek astronomer, mathematician, scholar, and student of Archytas and Plato. All of his original works are lost, though some fragments are ...

. Archytas and Eudoxus' student was

Menaechmus :''There is also a Menaechmus in Plautus' play, ''The Menaechmi''.'' Menaechmus ( el, Μέναιχμος, 380–320 BC) was an ancient Greek mathematician, geometer and philosopher born in Alopeconnesus or Prokonnesos in the Thracian Chersonese, w ...

. As a Pythagorean, Archytas believed that only arithmetic, not geometry, could provide a basis for satisfactory proofs. Archytas is believed to be the founder of mathematical

mechanics Mechanics (from Ancient Greek: μηχανική, ''mēkhanikḗ'', "of machines") is the area of mathematics and physics concerned with the relationships between force, matter, and motion among physical objects. Forces applied to objects r ...

.: ''Vitae philosophorum'' As only described in the writings of

Aulus Gellius Aulus Gellius (c. 125after 180 AD) was a Roman author and grammarian, who was probably born and certainly brought up in Rome. He was educated in Athens, after which he returned to Rome. He is famous for his ''Attic Nights'', a commonplace book, or ...

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. This machine, which its inventor called ''The pigeon'', may have been suspended on a wire or pivot for its flight. Archytas also wrote some lost works, as he was included by

Vitruvius Vitruvius (; c. 80–70 BC – after c. 15 BC) was a Roman architect and engineer during the 1st century BC, known for his multi-volume work entitled ''De architectura''. He originated the idea that all buildings should have three attribute ...

in the list of the twelve authors of works of mechanics. Thomas Nelson Winter presents evidence that the pseudo-Aristotelian '' Mechanical Problems'' was actually authored by Archytas and misattributed. Archytas named the

harmonic mean In mathematics, the harmonic mean is one of several kinds of average, and in particular, one of the Pythagorean means. It is sometimes appropriate for situations when the average rate is desired. The harmonic mean can be expressed as the recipro ...

, important much later in

projective geometry In mathematics, projective geometry is the study of geometric properties that are invariant with respect to projective transformations. This means that, compared to elementary Euclidean geometry, projective geometry has a different setting, pro ...

and

number theory Number theory (or arithmetic or higher arithmetic in older usage) is a branch of pure mathematics devoted primarily to the study of the integers and arithmetic function, integer-valued functions. German mathematician Carl Friedrich Gauss (1777� ...

, though he did not invent it. According to

Eutocius Eutocius of Ascalon (; el, Εὐτόκιος ὁ Ἀσκαλωνίτης; 480s – 520s) was a Palestinian-Greek mathematician who wrote commentaries on several Archimedean treatises and on the Apollonian ''Conics''. Life and work Little is ...

, Archytas solved the problem of

doubling the cube Doubling the cube, also known as the Delian problem, is an ancient geometric problem. Given the edge of a cube, the problem requires the construction of the edge of a second cube whose volume is double that of the first. As with the related pro ...

(the so-called Delian problem) in his manner (though he believed "that only arithmetic, not geometry", could provide a basis for satisfactory proofs) with a geometric construction.

Hippocrates of Chios Hippocrates of Chios ( grc-gre, Ἱπποκράτης ὁ Χῖος; c. 470 – c. 410 BC) was an ancient Greek mathematician, geometer, and astronomer. He was born on the isle of Chios, where he was originally a merchant. After some misadve ...

before, reduced this problem to finding mean proportionals. Archytas' theory of proportions is treated in book VIII of

Euclid Euclid (; grc-gre, Wikt:Εὐκλείδης, Εὐκλείδης; BC) was an ancient Greek mathematician active as a geometer and logician. Considered the "father of geometry", he is chiefly known for the ''Euclid's Elements, Elements'' trea ...

's '' Elements'', where is the construction for two proportional means, equivalent to the extraction of the

cube root In mathematics, a cube root of a number is a number such that . All nonzero real numbers, have exactly one real cube root and a pair of complex conjugate cube roots, and all nonzero complex numbers have three distinct complex cube roots. Fo ...

. According to

Diogenes Laërtius Diogenes Laërtius ( ; grc-gre, Διογένης Λαέρτιος, ; ) was a biographer of the Ancient Greece, Greek philosophers. Nothing is definitively known about his life, but his surviving ''Lives and Opinions of Eminent Philosophers'' is a ...

, 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.

blamed Archytas for his contamination of geometry with mechanics (

Plutarch Plutarch (; grc-gre, Πλούταρχος, ''Ploútarchos''; ; – after AD 119) was a Greek Middle Platonist philosopher, historian, biographer, essayist, and priest at the Temple of Apollo in Delphi. He is known primarily for his ''P ...

''Symposiacs'', Book VIII, Question 2
): ''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.'' Politically and militarily, Archytas appears to have been the dominant figure in Tarentum in his generation, somewhat comparable to

Pericles Pericles (; grc-gre, Περικλῆς; c. 495 – 429 BC) was a Greek politician and general during the Golden Age of Athens. He was prominent and influential in Athenian politics, particularly between the Greco-Persian Wars and the Pelopo ...

Athens Athens ( ; el, Αθήνα, Athína ; grc, Ἀθῆναι, Athênai (pl.) ) is both the capital and largest city of Greece. With a population close to four million, it is also the seventh largest city in the European Union. Athens dominates ...

a half-century earlier. The Tarentines elected him ''

strategos ''Strategos'', plural ''strategoi'', Linguistic Latinisation, Latinized ''strategus'', ( el, στρατηγός, pl. στρατηγοί; Doric Greek: στραταγός, ''stratagos''; meaning "army leader") is used in Greek language, Greek to ...

'', '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 Tarentine campaigns against their southern Italian neighbors. The ''

Seventh Letter The ''Seventh Letter of Plato'' is an epistle that tradition has ascribed to Plato. It is by far the longest of the epistles of Plato and gives an autobiographical An autobiography, sometimes informally called an autobio, is a self-writte ...

'' of

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 The philosopher king is a hypothetical ruler in whom political skill is combined with philosophical knowledge. The concept of a city-state ruled by philosophers is first explored in Plato's ''Republic'', written around 375 BC. Plato argued that ...

, 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 Dionysius II?).

Notes

References

External links

* *
Pseudo-Aristotle, ''Mechanica''
– Greek text and English translation
Complete fragments (Greek–Spanish bilingual edition)

Fragments and Life of Archytas
{{DEFAULTSORT:Archytas 428 BC births 347 BC deaths 4th-century BC philosophers Ancient Greek generals Ancient Greek mathematicians Ancient Greek music theorists Ancient Greek physicists Ancient Greek inventors Ancient Tarantines Pythagoreans Pythagoreans of Magna Graecia 5th-century BC mathematicians 4th-century BC mathematicians

Life and work

Notes

References

Further reading

External links