ARCHIMEDES

born c. 290280 BC, , Sicily [now in Italy] died 212/211 BC, Syracuse the most famous mathematician and inventor of ancient Greece. Archimedes is especially important for his discovery of the relation between the surface and volume of a sphere and its circumscribing cyclinder. He is known for his formulation of a hydrostatic principle (known as Archimedes' principle) and a device for raising water, still used in developing countries, known as the Archimedes screw. born c. 290, 280 BC, Syracuse, Sicily [now in Italy] died 212/211 BC, Syracuse the most famous mathematician and inventor of ancient Greece. Archimedes is especially important for his discovery of the relation between the surface and volume of a sphere and its circumscribing cylinder. He is also known for his formulation of a hydrostatic principle (known as Archimedes' principle) and a device for raising water, known as the Archimedes screw. Except for a brief period early in his career in Alexandria, Egypt, Archimedes spent most of his life in the Greek city-state of Syracuse. War machines of his construction greatly delayed the capture of the city by Roman forces in 212 or 211 BC, at which time Archimedes was killed by a Roman soldier. Archimedes won great renown for his inventions, such as the Archimedes screw and two astronomical globes, but the veracity of several anecdotes about his life is uncertain. For example, although his war machines were long successful against the Romans, it is doubtful that he constructed an array of mirrors to burn their ships. Archimedes' theoretical work that could be simply expressedsuch as the formulas for the surface area and volume of a spherebecame mathematical commonplaces, and one of the bounds that he established for pi, 22/7, was adopted as the usual approximation into the Middle Ages. But he had little influence on the development of mathematics until the science was revived by the Arabs in the 8th or 9th century and the Europeans in the 16th and 17th centuries. There are nine known extant treatises in Greek by Archimedes, and the references of later authors indicate that he had written a number of other works that are now lost. Of the known works, five are of particular interest. On the Sphere and Cylinder contains his discovery that the volume of a sphere is two-thirds that of the cylinder in which it is inscribed and that the surface area of a sphere is four times that of its greatest circle. A short work, Measurement of the Circle, contains his accurate and rational approximations of the value of pi and of the square roots of several numbers. On Floating Bodies, which survives only partly in Greek, is the first known work in hydrostatics, of which Archimedes is the recognized founder. It contains the work leading to Archimedes' principlethat a solid denser than a fluid will, when immersed in that fluid, be lighter by the weight of the fluid it displaces. The Sand-Reckoner remedies the inadequacies of the Greek numerical notational system by creating a place-value system of notation. Method Concerning Mechanical Theorems describes the mechanical technique used by Archimedes to arrive at the values proved mathematically in On the Sphere and Cylinder. The author's hope that this treatise would lead other mathematicians to new discoveries was unfulfilled because the work was lost until the 19th century. Additional reading The standard edition in Greek and Latin of the works of Archimedes with the ancient commentaries is J.L. Heiberg and Euangelos S. Stamates (eds.), Opera omnia, cum commentariis Eutocii, 3 vol. (191015, reprinted 1972). To the reprint was added ber einander berhrende Kreise (1975), a translation into German by Y. Dold-Samplonius, H. Hermelink, and M. Schramm of the Arabic text On Tangent Circles. T.L. Heath (ed.), The Works of Archimedes (1897), and a supplement, The Method of Archimedes (1912)reprinted together under the first title (1953)are English translations; unfortunately Heath, by paraphrasing Archimedes' mathematics in modern notation, misrepresents him. Paul Ver Eecke, Les Oeuvres compltes d'Archimde (1921), provides a much better translation retaining the essence of the original.The best detailed discussion of the contents of Archimedes' work is E.J. Dijksterhuis, Archimedes (1956, reissued 1987), which also assembles most of the biographical data. Marshall Clagett, Archimedes, in Charles Coulston Gillispie (ed.), Dictionary of Scientific Biography, vol. 1 (1970), pp. 213231, is particularly valuable for its bibliography and discussion of the influence of Archimedes. On the textual tradition and knowledge of Archimedes in Europe in the Middle Ages and early Renaissance, Marshall Clagett (ed.), Archimedes in the Middle Ages (196480), contains indispensable information. Catherine Osborne, Archimedes on the Dimension of the Cosmos, Isis, vol. 74, no. 272, pp. 234242 (June 1983), satisfactorily explains for the first time the basis of Archimedes' numbers for the planetary distances. Gerald J. Toomer The Editors of the Encyclopdia Britannica