a celebrated geometrician, born at Syracuse in the island of Sicily, and related to Hiero king of Syracuse. He was remarkable for his extraordinary application to mathematical studies; in which he used to be so much engaged, that his servants were often obliged to take him from thence by force. He had such a surprising invention in mechanics, that he affirmed to Hiero, if he had another earth, wherein to plant his machines, he could move this which we inhabit. He is said to have formed a glass sphere, of a most surprising workmanship, wherein the motions of the heavenly bodies were represented. He discovered the exact quantity of the silver which a goldsmith had mixed with the gold, in a crown he had made for the king: he had the hint of this discovery from his perceiving the water rise up the sides of the bath as he went into it, and was filled with such joy, that he ran naked out of the bath, crying, "I have found it! I have found it!" By the invention of machines, he, for a long time, defended Syracuse *, on its being besieged by Marcellus. On the city's being taken, that general commanded his soldiers to have a particular regard to the safety of this truly great man; but his care was ineffectual. "What gave Marcellus the greatest concern (says Plutarch), was the unhappy Archimedes, who was at that time in his museum, and his mind, as well as his eyes, so fixed and intent upon some geometrical figures, that he neither heard the noise and hurry of the Romans, nor perceived the city was taken. In this depth of study and contemplation, a soldier came suddenly upon him, and commanded him to follow him to Marcellus; which he refusing to do till he had finished his problem, the soldier, in a rage, drew his sword, and ran him through the body." Others have related the circumstances of his death in a somewhat different manner. It however happened 208 years before the Christian era. Cicero, when he was quaestor in Italy, Archimedes discovered his tomb, on which was carved a cylinder and sphere. Some of the works of this great mathematician are lost, but others are preserved. His pieces which remain are, 1. Two books of the Sphere and Cylinder. 2. The Dimensions of a Circle. 3. Of Centres of Gravity, or Equipoise. 4. Of Spheroids and Conoids. 5. Of Spiral Lines. 6. The Quadrature of a Parabola. 7. Of the Number of the Sand. 8. Of Bodies that float on Fluids. The best edition of these is that published at London, in 1675, 4to.

Among the works of Archimedes which are lost, we may reckon the descriptions of the following inventions, which we may gather from himself and other ancient authors:

1. His account of the method which he used to discover the mixture of gold and silver in the crown. 2. His description of the syphon, an engine to draw water out of places where it is stagnated. 3. Athenæus, speaking of the prodigious ship built by the order of Hiero, tells us, that Archimedes invented the coehion, by means of which the hold, notwithstanding its depth, could be drained by one man. 4. Diodorus Siculus informs us (lib. v.) that he contrived this machine to drain Egypt, and that by a wonderful mechanism it would empty the water from any depth. 5. The syphon, by means of which (according to Athenæus, lib. v.) he launched Hiero's great ship. 6. The terræmotive, of the power of which Tzetzes gives a hyperbolical relation, Chil. ii. hist. 35. 7. The machines he used in the defence of Syracuse against Marcellus. Of Archimedes we have an account in Polybius, Livy, and Plutarch. 8. His burning-glares, with which he is said to have set fire to the Roman galleys. 9. Galen, lib. iii. 10. His pneumatic and hydraulic engines, concerning which he wrote books, according to Tzetzes, Chil. ii. hist. 35.