ARCHIME'DES, the most celebrated of ancient mathematicians, was b. at Syracuse about 287 B.C. He is said to have been a kinsman of king Hiero, though he does not seem to have held any public office, but devoted himself entirely to science. In regard to mathematics, we cannot estimate fully the merits of A. without a more exact knowl edge of the state of the science as he found it; we know, however, that he enriched it with discoveries of the highest importance, on which modern mathematicians have founded their methods of measuring curved surfaces and solids. Euclid only considers a few curved figures in relation to one another, but without comparing them with recti lineal surfaces and solids. The thebrems necessary to this transition are laid down by A. in his treatises "on the Sphere and Cylinder," "on Spheroids and Conoids," and " on the Measurement of the Circle." His demonstration that the area of a segment of a parabola is two thirds of the inclosing parallelogram, is the first real example of the quadrature (q.v.) of a curvilinear space. In his treatise on spirals, he rises to yet higher investigations, which, however, are not very easily understood even by masters of the subject.
A. is the only one of the ancients that contributed anything satisfactory on the theory of mechanics and on hydrostatics. He first established the truth, that a body plunged in a fluid loses as much of its weight as is equal to the weight of an equal vol lume of the fluid. (See the following article.) It was by this law that he determined how much alloy the goldsmith, whom Hiero had commissioned to make a crown of pure gold, had fraudulently mixed with the metal. The solution of the problem suggested itself to him as he was entering the bath, and he is reported to have been so overjoyed as to hasten home without waiting to dress, exclaiming: "I have found it 1 I have found it!" (Eureka ! Eureka!) Practical mechanism seems to have been an equally new science in the days of A. ; for his boast, that if he had a fulcrum or stand-point, he could move the world, betrays the enthusiasm with which the extraordinary effects of his newly invented machines inspired him. Among the numerous inventions ascribed to A., is
that of the endless screw, and the cochlea or water-screw (see AucnimEnEs' ScuEw), in which the water made in a manner to ascend by its own gravity. During the siege of Syracuse by the Romans, he exerted all his ingenuity to the defence of the city. Poly bins, Livy, and Plutarch speak with astonishment of the machines with which he Opposed the attacks of the enemy. But while giving detailed accounts of his other con trivances, they say nothing of his having set fire to the ships by means of mirrors, a story which is not very probable in itself, and rests on later narratives. When the Romans took the city by surprise (212 n.c.), A., according to the tradition, was sitting in the public square lost in thought, with all sorts of geometrical figures before him drawn in the sand. As a Roman soldier rushed upon him, he called out to him not to spoil the circle! But the rude warrior cut him -down. According to his own direction, a cylin der inclosing a sphere was engraved upon his tombstone, in commemoration of his discovery of the relation between these solids—a discovery on which he set particular value. When Cicero was in Sicily as questor, he discovered the tomb hid among briers. Ills collected extant works were edited by Torelli (Oxf. 1792). There is a French trans lation with notes by F. Peyrard (Paris, 1808, 2 vols.), and one in German by Nizze (Strals. 1824). The Arenamus was translated,into English by G. Anderson (Lond. 1784). The object of the treatise is to prove that it is possible to assign a number greater than that of the grains of sand that would fill the sphere of the fixed stars, the diameter of which A. assumes at a certain number of stadia. The difficulty lay in expressing such a vast number by means of the clumsy notation of Greek arithmetic, and the device by which the difficulty is eluded is considered as affording a striking instance of A.'s genius.