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translated from the Dutch in Gilbert's 6< Annalen der Physik," vol. liii. p. 242. The most probable conclusion seems to be, that Archimedes had on some occasion set fire to a ship or ships by means of a burning mirror, and that later writers falsely connected the circumstance with the siege of Syracuse. (See Ersch and Gruber's Cyclop, art. Arcldin. note, and Gibbon, chap. 40.)
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 cup^/ccc, eupijKcc. 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 »vas at this time acquainted with the theorems lemonstrated in his hydrostatical treatise con-:erning the loss of weight of bodies immersed in
•vater, since he would hardly have evinced such ively gratification at the obvious discovery that hey might be applied to the problem of the crown; is delight must rather have arisen from his now rst catching sight of a line of investigation which id immediately to the solution of the problem i question, and ultimately to the important leorems referred to. (Vitruv. ix. 3.; Proclus. ^omm. in lib. i. Eucl. ii. 3.) He superintended the building of a ship of ex-
•aordinary size for Hiero, of which a description given in Athenaeus (v. p. 206, d), where he is so said to have moved it to the sea by the help
• a screw. According to Proclus, this ship was .tended by Hiero as a present to Ptolemy ; it may )ssibly have been the occasion of Archimedes' sit to Egypt.
He invented a machine called, from its form, Dchlea, and now known as the water-screw of rchimedes, for pumping the water out of the hold this vessel; it is said to have been also used in >ypt by the inhabitants of the Delta in irrigating eir lands. (Diod. i. 34; Vitruv. x. 11.) An vestigation of the mathematical theory of the iter screw is given in Ersch and Gruber. The :abian historian Abulpharagius attributes to :chimedes the raising of the dykes and bridges sd as defences against the overflowing of the le. (Pope-Blount, Censure^ p. 32.) Tzetzes il Oribasius (de MacJi. xxvi.) speak of his Tris-s£, a machine for moving large weights; probably :ombination of pulleys, or wheels and axles. A Iraulic organ (a musical instrument) is mention-by Tertullian (de Anima^ cap. 14), but Pliny i. 37) attributes it to Ctesibius. (See also Pap-;, Math. Coll. lib. 8, introd.) An apparatus led loculus^ apparently somewhat resembling the inese puzzle^ is also attributed to Archimedes. )rtunatianus, de Arte Metrica, p. 2684.) His st celebrated performance was the construction a spltere; a kind of orrery, representing the
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movements of the heavenly bodies, of which we have no particular description. (Claudian, Epigr. xxi. in Spliaeram Archimedis; qic.Nat. Deor.ii. 35, tusg. Disp. i. 25 ; Sext. Empir. adv. Math. ix. 115 j Lactant. Div. Inst. ii. 5 ; Ov. Fast. vi. 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. xxv. 31; Valer. Max. viii. 7. § 7; Pint. Marcell. 19 ; Cic. de, fin. v. 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. v. 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 Avhich other intellectual gifts are comparatively fruitless. (See the introd. to the treatise " De Con. et Sphaer.") It may be noticed that he resembled other great thinkers, in his habit of complete abstraction from outward things, when reflecting on ubjects 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. (Pint. I. 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. 220, c. d.) The success of Archimedes in conquering difficulties seems to have made the expression Trp6€\r){j.a 'Ap-XWnSziov proverbial. (See Cic. ad Att. xiii. 28, pro Cluent. 32.)
The following works of Archimedes have come down to us: A treatise on Equiponderants and Centres of Gravity^ in which the theory of the equilibrium of the straight lever is demonstrated, both for commensurable and incommensurable weights; and various properties of the centres of gravity of plane surfaces bounded by three or four straight lines, or by a straight line and a parabola, are established.
The Quadrature of the Parabola, in which it is proved, that the area cut off from a parabola by
