ARCHIMEDES (Gk. 'Apvi.vjans. Archimedes) ( B.C. 287-212). A Greek geometrician and mechanician, the greatest mathematician of an tiquity. He was born in the State of Syracuse, in the Island of Sicily. He studied probably under Conon at the University of Alexandria, spending the major part of his life in Sicily. He was killed in the sack of Syracuse. The most im portant among his extant works include three on plane geometry, three on solid geometry, one on arithmetic, and three on mechanics. In the treatise on the measurement of the circle, the value of w is given as a number less than 31 and greater than 310. He also gave formillas for the area of the circle and the ellipse, and for the sector of a spiral whose equation is r — His demonstration that the area of a segment of a parabola is two-thirds that of the inclosing parallelogram is the first real example of the quadrature (q.v.) of a curvilinear surface. His method of exhaustion is suggestive of the modern methods of calculus. In the works on solid geometry are treated the volumes of spheroids and colloids. His arithmetical work, known by
its Latin title, Arenarins (sand-reckoner), con tains his famous attempt to express the amount of sand required to fill the universe. This work has given rise to the conjecture that Archimedes invented a new- and powerful system of notation, all knowledge of which perished with the work itself. Besides his work in pure mathematics, Archimedes also made valuable contributions to applied mathematics, including applications of geometry to the theory of machines, as levers, pulleys, and screws. He also improved the methods of finding centres of gravity. In accord ance with a wish of Archimedes, Marcellus raised in h is honor a tomb, on MIMh was engraved a sphere inscribed in a cylinder. Cicero, in his Tuscan Disputations, gives a charming account of his discovery of the tomb in B.C. 75. The most noted edithms of Archimedes' works are those of .1. Torelli (Oxford. 1792) ; J. L. Heiberg (Leipzig, 1881) : and T. L. Heath (Cambridge, 1897).