ARCHYTAS (c. 428—347 B.C.)  , of Tarentum, Greek philosopher and scientist of the Pythagorean school, famous as the intimate friend of Plato, was the son of Mnesagoras or Histiaeus . Equally distinguished in natural science,philosophy and the administration of civic affairs, he takes a high place among the versatile savants of the ancient Greek world . He was a man of high character and benevolent disposition, a fine flute-player, and a generous master to his slaves, for whose children he invented the rattle . He took a prominent part in state affairs, and, contrary to precedent, was seven times elected commander of the army . Under his leadership, Tarentum fought with unvarying success against the Messapii, Lucania and even Syracuse . After a life of high intellectual achievement and uninterrupted public service, he was drowned (according to a tradition suggested by Horace, Odes, i . 28) on a voyage across the Adriatic, and was buried, as we are told, at Matinum in Apulia . He is described as the eighth leader of the Pythagorean school, and was a pupil (not the teacher, as some have maintained) of Philolaus . In mathematics, he was the first to draw up a methodical treatment of mechanics with the aid of geometry; he first distinguished harmonic progression from arithmetical and geometrical progressions . As a geometer he is classed by Eudemus, the greatest ancient authority, among those who " have enriched the science with original theorems, and given it a really sound arrangement." He evolved an ingenious solution of the duplication of the cube, which shows considerable knowledge of the generation of cylinders and cones . The theory of proportion, and the study of acoustics and music were considerably advanced by his investigations . He was said to be the inventor of a kind of flying-machine, a wooden pigeon balanced by a weight suspended from a pulley, and set in motion by compressed air escaping from a valve.' Fragments of his ethical and metaphysical writings are quoted by Stobaeus, Simplicius and others .

To portions of these

Aristotle has been supposed to have been indebted for his doctrine of the categories and some of his chief ethical theories . It is, however, certain that these fragments are mainly forgeries, attributable to the eclecticism of the 1st or 2nd century A.D., of which the chief characteristic was a desire to father later doctrines on the old masters . Such fragments as seem to be authentic are of small philosophical value . It is important to notice that Archytas must have been famous as a philosopher, inasmuch as Aristotle wrote a special treatise (not extant) On the Philosophy of Archytas . Some positive idea of his speculations may be derived from two of his observations: the one in which he notices that the parts of animals and plants are in general rounded in form, and the other dealing with the sense of hearing, which, in virtue of its limited receptivity, he compares ' If this be the proper translation of Aulus Gellius, Noctes Atticae, X . 12..9," . . . simulacrum columbae e ligno . . factum; ita erat scilicet libramentis suspensum et aura spiritus inclusa atque occulta concitum." (See AERONAUTICS.)with vessels, which when filled can hold no more . Two important principles are illustrated by these thoughts, (I) that there is no absolute distinction between the organic and the inorganic, and (2) that the argument from final causes is no explanation of phenomena . Archytas may be quoted as an example of Plato's perfect ruler, the philosopher-king, who combines practical sagacity with high character and philosophic insight . See G . Hartenstein, De Arch .

Tar. frag . (Leipzig, 1833) ; O . F . Gruppe, Uber d . Frag. d . Arch . (184o); F . Beckmann, De Pythag. reliq . (Berlin, 1844, 1850) ; Egger, De Arch . Tar. vit., op . Phil . ; Ed .

Zeller, Phil. d . Griech . ; Theodor Gomperz, Greek Thinkers, ii . 259 (Eng. trans . G . G . Berry, Lond., 1905) ; G . J . Allman, Greek Geometry from Tholes to Euclid (1889); Florian Cajori, History of Mathematics (New York, 1894) ; M . Cantor, Gesch. d. gr . Math . (1894 fell.) .

The mathematical fragments are collected by Fr .

Blass, Melanges Graux (Paris, 1884) . For Pythagorean mathematics see further PYTHAGORAS . _ ARCIS-SUR-AUBE, a town of eastern France, capital of an arrondissement in the department of Aube, on the left bank of the Aube, 23 M . N. of Troyes on the Eastern railway to ChaIonssur-Marne . Pop . (1906) 2803 . Fires in 1719, 1727 and 1814 destroyed the ancient buildings, and it is now a town built in modern style with wide and regular streets . A chateau of the 18th century occupies the site of an older one in which Diana of Poitiers, mistress of Henry II., resided . The only other building of interest is the church, which dates from the i5th century . In front of it there is a statue of Danton, a native of the town . Arcis-sur-Aube has a tribunal of first instance .

Its

industries include -important hosiery manufactures, and it carries on trade in grain and coal . The town communicates with Paris by means of the Aube, which becomes navigable at this point . A battle was fought here on the 20th and 21st of March 1814 between Napoleon and the Austro-Russian army under Schwarzenberg (see NAPOLEONIC CAMPAIGNS) .