ARCHIMEDES (’Αρχιμηδης)—mathematician, mechanical engineer, and inventor, one of the most famous learned men of ancient times, b. around 287 BC in Syracuse in Sicily, d. in 212 BC also in Sicily.

He came from a family with scientific traditions. His father Phidias was an astronomer (he measured the angular diameter of the Sun and Moon). In Alexandria he studied under scholars such as Eratosthenes (with whom he probably collaborated in measuring the length of the Earth’s meridian) and Conon of Samos (to whom later he would often send his mathematical works before publication); he corresponded with a disciple of Conon, Dositheus of Pelusium, but probably did not know him personally. During his studies he traveled though Egypt and probably through Spain. During the second Punic war he effectively directed the defense of Syracuse for two years against the Roman armies led by Marcellus. To this purpose, Archimedes designed and used many defensive machines. Among his contemporaries Archimedes was famous primarily as the builder of devices such as the helical hydraulic pump (Archimedes’ screw), a water clock, a water organ, a planetarium, a compound pulley, and systems of spherical mirrors.

Archimedes wrote in a laconic style, often leaving out important elements of his reasoning. His most important accomplishments in mathematics include a method of exhaustion that allow him to show the volume of geometrical solids bounded by arbitrary surfaces and the centers (centroids) of the surfaces of figures bounded by arbitrary curves. The method of exhaustion and the so-called axiom of Archimedes (presented in his treatise On the sphere and cylinder) which says, given two magnitudes having a ratio, one can find a multiple of either which will exceed the other. This axiom became a source of new mathematical ideas in modern mathematics (differential calculus and integral calculus) and in contemporary mathematics (non-standard analysis). Archimedes regarded as his greatest accomplishment the work On the sphere and cylinder in which he proved, among other things, that the volume of a sphere is 2/3 the volume of the smallest cylinder that can contain it. Another accomplishment of his was the calculation of the number π, i.e., the relation of the circumference of a circle to its diameter. (3 10/71 < π < 3 1/7).. Archimedes was also the author of the principles of statics (the concept of force, the principles of a crane’s operation) and hydrostatics (Archimedes’ law).

The ideas contained in Archimedes’ works inspired scholars throughout the ages, but had an especially strong influence in modern science when his work were first printed (Ve 1503, 1543): The measuring of the circle and The squaring of the parabola in the original version with the Latin translation of William of Moerbecke. Soon thereafter (Bas 1544) Thomas Geschauff (Lat. Venatorius 1490–1551) published the Greek text of all Archimedes’ works known at the time, including the commentary of Eutakios. This edition included the Latin translation of Jacob of Cremona and was edited by Regiomontanus (Johann Müller 1436–1476).

Today there are widely varied interpretations of Archimedes’ philosophical position because of the absence of clear philosophical statements in his writings. Some authors (J. Schneider) treat him as an authentic prototype of the technocrat or a pure mathematician oriented toward the Pythagorean philsophy of nature; some (P. Delesdime) see more Aristotelian influences than Pythagorean influences in his conception of infinity; some authors (A. Virieux-Reymond) see the influence of Platonism on his scientific method or regard him (S. I. Luria) as a dialectical materialist inspired by the atomist doctrine of Democritus. Some (O. Pedersen) see him as the author of a third ancient conception of science after Plato’s and Aristotle’s. According to this conception, natural phenomena are not connected by metaphysical relations expressed by causes and effects, but by mathematical relation of a non-metaphorical character (without causal or teleological conditions).

An annotated critical edition of Archimedes’ works was published by J. L. Heiberg: Archimedis opera (I–III, L 1880–1881, 1910–1915², reprinted with corrections and supplements by E. S. Stamatis, I–IV, St 1972). T. L. Heath published an English translation along with a treatise discovered by Heiberg On method: The Works of Archimedes C C 1987, repr. The Works of Archimedes. A Supplement, The Method of Archimedes of 1912, NY 1976.

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Zenon E. Roskal

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