Archytas de Tarente

Biography

Archytas, wire of Mnésagore or Histiaïos (Diogène Laërce, VIII, 79), were born with Tarente, in Grande Greece (Italy).

Scientist of the school pythagorician, he was the disciple of Philolaos of Crotona and would have studied with Métaponte, then became professor of Mathématiques of Eudoxe de Cnide. He was the close friend of Plato: Plato saw it several times between 390 and 350 in Sicily and Italy, and was saved by him death which Denys prepared to him. The influence of Archytas on the thought of Plato is undoubtedly considerable, although it is difficult to measure all the extent of it. Archytas had Empédocle and Ménechme for disciples (this last was also the disciple of Eudoxe).

The most important character of Tarente, it had, in spite of the law, seven times the supreme command of his Cité (it was Stratège from 367 to 361) which had a democratic mode then, and it directed the league of the Italians of Large Greece (according to the Souda). Its political success and its benevolence were engraved in the memories of all (Pseudo-Démosthène, Discours on the love , LXI, 46) and its memory was transmitted until the end of the Roman République (a treaty of Cicéron testifies thus to the heritage pythagorician in Italy). Tarente was then the last bastion of the pythagoricians, and Archytas made of it a powerful city to which it applied the ideas of Pythagore:

“the inhabitants of Tarente held an extraordinary power thanks to the adoption of a democratic constitution. They gave in addition their adhesion to the philosophy of Pythagore and particularly Archytas which remained very a long time with the head of the city. ” (Strabon, VI, 280)

He resigns of his functions into 360, perhaps to lay out of more than spare time and to be able to study. (cf Letter of Plato with Archytas ).

He died in a shipwreck on the coasts of the Apulie, dead that Horace evokes in a Ode which indicates the site of its tomb:

“You which measured the sea and the ground and the infinite number of the grains of sand, Archytas, entire covers you the humble gift of a little dust close to the broad sides to Matinus, and it does not make use of nothing to have explored the air residences and to have traversed the vault of the sky, of a heart intended for death. ” (delivers I, XXVIII)

Philosophy

Few testimonys which we have on his thought shows that Archytas conceived the Mathématiques (and in particular the Calcul) like a Art applicable to all the problems:

“It seems well that the art of the calculation reported to philosophy is quite higher than other arts, from its capacity to be treated, better still than the geometry does it, any problem with a larger certainty. ” (Stobée, Choice of texts , I, foreword)

However, this art of calculation has an ethical virtue:

“the disagreement ceased and the harmony increased day when the way of calculating was invented. Thanks to him indeed, instead of the spirit of higher bid, it is the equality which reigns; it is still him which puts agreement with those to us with which we treat business. ” (Stobée, IV, 1,139)

One can thus suppose that it is according to this Théorie that Archytas controlled its city, by maintaining the balance and the equality of the parties. Besides it treated its servants with largest humanity.

Ethical

Cicéron brings back a talk of Archytas to us on passions:

“Caton: You, young men, who are among the best, listen to the language of Archytas de Tarente, a great man and who counts among the most distinguished spirits. Its words to me were reported when, any young person still, I was in Tarente with Fabius Maximus. Archytas said that no more disastrous present, more ruinous than the pleasure was not made to the men, the pleasure with the conquest of which the appetite goes without measurement and reflection. ”

If the authenticity of these talks can be questioned, on the other hand its contents, in conformity with the rationality of Archytas, are confirmed by several testimonys on its Vie: Archytas, indeed, was capable of a great control of its Passion S, in particular of the Colère.

Physics

Archytas thought that the place and the body are unlimited:

“If I were in extreme cases of the sky, in other words on the spheres of the fixed ones, could I tend with-outside the hand or a stick, yes or not? Admittedly, it is absurd that I cannot do it; but if I reach that point, that implies the existence of an outside, body or place. ” (according to Eudème, quoted by Simplicius de Cilicie, Comment on the Physics of Aristote , 467,26)

Mathematics

A quotation of Porphyre of Tyr teaches us that Archytas considered that the mathematicians were to know astronomy, the geometry, the arithmetic one, the spherical one and the music, because these disciplines are sisters . This formula was taken again by Plato ( the Republic , 530d):

“These disciplines are sisters, as say it Pythagoriciens and as we admit it too. ”

He is sometimes recognized as being the founder of the named part of the Mathématiques the Mécanique that he systematized (Diogène Laërce, VIII, 83), and one allots the merit to have given to him more rigor to mathematics. According to Eutocius ( Comment on sphere and cylinder of Archimedes , II) Archytas solved the problem of the Duplication of the cube in a manner which is clean for him with a geometrical construction. Hippocrates de Chios before, reduced this problem to a search for report/ratio of Proportion S. the theory of Archytas of the proportions is treated in book VIII of the Éléments of Euclide.

The Courbe of Archytas, which is used in its solution of the problem of the duplication of the cube, was named in its honor.

Music

Archytas seems to be the pythagorician who was interested the most in the Musique, and he would have invented a physical theory of the his.

The inventor

Archytas was interested in the applications of sciences, interest whose Plato blamed it. One thus allots to Archytas several inventions of which a dove out of wooden able to fly (Favorinus, quoted by Aulu-Cold, Nuits attics , X, XII, 8).

One also allots to him the invention of the Crécelle:

“thus Let us regard as a happy invention the rattle of Archytas, which one gives to the small children to occupy them; that avoids all to them breaking in the house, because youth is not able to remain in place. ” ( Political , VIII, VI, 1340 B 26)

Works

He wrote books in many fields: music and mathematics, on the machines, the Agriculture.

Of the decade
Of mathematics
Treated music
Of the flutes
Talks

Random links: