(Ἀρχιμήδης), of Syracuse, the most famous of ancient mathematicians, was born B. C. 287, if the statement of Tzetzes, which makes him 75 years old at his death, be correct.
Of his family little is known. Plutarch calls him a relation of king Hiero; but Cicero (Tusc. Disp. 5.23), contrasting him apparently not with Dionysius (as Torelli suggests in order to avoid the contradiction), but with Plato and Archytas, says, " humilem homunculum a pulvere et radio excitabo." At any rate, his actual condition in life does not seem to have been elevated (Silius Ital. 14.343), though he was certainly a friend, if not a kinsman, of Hiero. A modern tradition makes him an ancestor of the Syracusan virgin martyr St. Lucy. (Rivaltus, in vit. Archim. Mazzuchelli, p. 6.) In the early part of his life he travelled into Egypt, where he is said, on the authority of Proclus, to have studied under Conon the Samian, a mathematician and astronomer (mentioned by Virg. Eel. 3.40), who lived under the Ptolemies, Philadelphus and Euergetes, and for whom he testifies his respect and esteem in several places of his works. (See the introductions to the Quadratura Paraboles and the De Helicibus.) After visiting other countries, he returned to Syracuse. (Diod. 5.37.) Livy (24.34) calls him a distinguished astronomer, "unicus spectator coeli siderumque;" a description of which the truth is made sufficiently probable by his treatment of the astronomical questions occurring in the Arenarius. (See also Macrob. Somn. Scip. 2.3.) He was popularly best known as the inventor of several ingenious machines; but Plutarch (Plut. Marc. 100.14), who, it should be observed, confounds the application of geometry to mechanics with the solution of geometrical problems by mechanical means, represents him as despising these contrivances, and only condescending to withdraw himself from the abstractions of pure geometry at the request of Hiero. Certain it is, however, that Archimedes did cultivate not only pure geometry, but also the mathematical theory of several branches of physics, in a truly scientific spirit, and with a success which placed him very far in advance of the age in which he lived. His theory of the lever was the foundation of statics till the discovery of the composition of forces in the time of Newton, and no essential addition was made to the principles of the equilibrum of fluids and floating bodies, established by him in his treatise " De Insidentibus," till the publication of Stevin's researches on the pressure of fluids in 1608. (Lagrange, Méc. Anal. vol. i. pp. 11, 176.)
He constructed for Hiero various engines of war, which, many years afterwards, were so far effectual in the defence of Syracuse against Marcellus, as to convert the siege into a blockade, and delay the taking of the city for a considerable time. (Plut. Marc. 15-18; Liv. 24.34; Plb. 8.5_9.) The accounts of the performances of these engines are evidently exaggerated; and the story of the burning of the Roman ships by the reflected rays of the sun, though very current in later times, is probably a fiction, since neither Polybius, Livy, nor Plutarch gives the least hint of it. The earliest writers who speak of it are Galen (De Temper. 3.2) and his contemporary Lucian (Hippias, 100.2), who (in the second century) merely allude to it as a thing well known. Zonaras (about A. D. 1100) mentions it in relating the use of a similar apparatus, contrived by a certain Proclus, when Byzantium was besieged in the reign of Anastasius ; and gives Dion as his authority, without referring to the particular passage. The extant works of Dion contain no allusion to it. Tzetzes (about 1150) gives an account of the principal inventions of Archimedes (Chil. 2.103-156), and amongst them of this burning machine, which, he says, set the Roman ships on fire when they came within a bow-shot of the walls; and consisted of a large hexagonal mirror with smaller ones disposed round it, each of the latter being a polygon of 24 sides. The subject has been a good deal discussed in modern times, particularly by Cavalieri (in cap. 29 of a tract entitled " Del Specchio Ustorio," Bologna, 1650), and by Buffon, who has left an elaborate dissertation upon it in his introduction to the history of minerals. (Oeuvres, tom. v. p. 301, &c.) The latter author actually succeeded in igniting wood at a distance of 150 feet, by means of a combination of 148 plane mirrors. The question is also examined in vol. ii. of Pevrard's Archimedes ; and a prize essay upon it by Capelle is
The following additional instances of Archimedes' skill in the application of science have been collected from various authors by Rivaltus (who edited his works in 1615) and others.
He detected the mixture of silver in a crown which Hiero had ordered to be made of gold, and determined the proportions of the two metals, by a method suggested to him by the overflowing of the water when he stepped into a bath. When the thought struck him he is said to have been so much pleased that, forgetting to put on his clothes, he ran home shouting εὕρηκα, εὕρηκα. The particulars of the calculation are not preserved, but it probably depended upon a direct comparison of the weights of certain volumes of silver and gold with the weight and volume of the crown; the volumes being measured, at least in the case of the crown, by the quantity of water displaced when the mass was immersed. It is not likely that Archimedes was at this time acquainted with the theorems demonstrated in his hydrostatical treatise concerning the loss of weight of bodies immersed in water, since he would hardly have evinced such lively gratification at the obvious discovery that they might be applied to the problem of the crown ; his delight must rather have arisen from his now first catching sight of a line of investigation which led immediately to the solution of the problem in question, and ultimately to the important theorems referred to. (Vitr. 9.3.; Proclus. Comm. in lib. i. Eucl. 2.3.)
He superintended the building of a ship of extraordinary size for Hiero, of which a description is given in Athenaeus (v. p. 206, D), where he is also said to have moved it to the sea by the help of a screw. According to Proclus, this ship was intended by Hiero as a present to Ptolemy; it may possibly have been the occasion of Archimedes' visit to Egypt.
He invented a machine called, from its form, Cochlea, and now known as the water-screw of Archimedes, for pumping the water out of the hold of this vessel; it is said to have been also used in Egypt by the inhabitants of the Delta in irrigating their lands. (Diod. 1.34; Vitr. 10.11.) An investigation of the mathematical theory of the water screw is given in Ersch and Gruber. The Arabian historian Abulpharagius attributes to Archimedes the raising of the dykes and bridges used as defences against the overflowing of the Nile. (Pope-Blount, Censura, p. 32.) Tzetzes and Oribasius (de Mach. xxvi.) speak of his Trispast, a machine for moving large weights; probably a combination of pulleys, or wheels and axles. A hydraulic organ (a musical instrument) is mentioned by Tertullian (de Anima, cap. 14), but Pliny (7.37) attributes it to Ctesibius. (See also Pappus, Math. Coll. lib. 8, introd.) An apparatus called loculus. apparently somewhat resembling the Chinese puzzle, is also attributed to Archimedes. (Fortunatianus, de Arte Metrica, p. 2684.) His most celebrated performance was the construction of a spbere : a kind of orrery, representing the movements of the heavenly bodies, of which we have no particular description. (Claudian, Epigr. xxi. in Sphaeram Archimedis; Cic. Nat. Deor. 2.35, Tutsc. Disp. 1.25; Sext. Empir. ad v. Math. 9.115 ; Lactant. Div. Inst. 2.5; Ov. Fast. 6.277.)
When Syracuse was taken, Archimedes was killed by the Roman soldiers, ignorant or careless who he might be. The accounts of his death vary in some particulars, but mostly agree in describing him as intent upon a mathematical problem at the time. He was deeply regretted by Marcellus, who directed his burial, and befriended his surviving relations. (Liv. 25.31; Valer. Max. 8.7.7; Plut. Marc. 19; Cic. de fin. 5.19.) Upon his tomb was placed the figure of a sphere inscribed in a cylinder, in accordance with his known wish, and in commemoration of the discovery which he most valued. When Cicero was quaestor in Sicily (B. C. 75) he found this tomb near one of the gates of the city, almost hid amongst briars, and forgotten by the Syracusans. (Tusc. Disp. 5.23.)
Of the general character of Archimedes we have no direct account. But his apparently disinterested devotion to his friend and admirer Hiero, in whose service he was ever ready to exercise his ingenuity upon objects which his own taste would not have led him to choose (for there is doubtless some truth in what Plutarch says on this point) ; the affectionate regret which he expresses for his deceased master Conon, in writing to his surviving friend Dositheus (to whom most of his works are addressed); and the unaffected simplicity with which he announces his own discoveries, seem to afford probable grounds for a favourable estimate of it. That his intellect was of the very highest order is unquestionable. He possessed, in a degree never exceeded unless by Newton, the inventive genius which discovers new provinces of inquiry, and finds new points of view for old and familiar objects; the clearness of conception which is essential to the resolution of complex phaenomena into their constituent elements; and the power and habit of intense and persevering thought, without which other intellectual gifts are comparatively fruitless. (See the introd. to the treatise " De Con. et Sphaer.") It maybe noticed that he resembled other great thinkers, in his habit of complete abstraction from outward things, when reflecting on subjects which made considerable demands on his mental powers. At such times he would forget to eat his meals, and require compulsion to take him to the bath. (Plut. l. c.) Compare the stories of Newton sitting great part of the day half dressed on his bed, while composing the Principia; and of Socrates standing a whole day and night, thinking, on the same spot. (Plat. Symp. p. 220c. d.) The success of Archimedes in conquering difficulties seems to have made the expression πρόβλημα Ἀρχιμήδειυν proverbial. (See Cic. Att. 13.28, pro Cluent. 32.)
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