the most celebrated of the ancient mathematicians, was born at Syracuse, in Sicily, about the year 180 before the Christian era. Hiero, king of Syracuse, deemed it an honour to have this philosopher for his relative and friend. History does not inform us to whom he was indebted for the rudiments of literature, but he flourished about 50 years after Euclid. It is reported that he was indebted to Egypt for much of his knowledge; but other accounts indicate that he conferred more knowledge than he received from that celebrated nation; and, in particular, Diodorus mentions that Egypt was indebted to him for the invention of the screw-pump for drawing off water; and the same author narrates that he was the inventor of several other useful machines, which conveyed his fame to every quarter of the globe. The following passage from Livy proves that he was dexterous both for the inventing of warlike machines, and also for his accurate observation of the heavenly bodies: "Unicus spectator coeli siderumque, mirabilior tamen inventor ac machinator bellicorum tormentorum," &c. lib. xxiv. cap. 34. It appears also that, in Cicero's time, he had become proverbial for his skill in solving problems. In a letter to Atticus, he informs him that he is now freed from a difficulty, which he termed an Archimedean problem, lib. xiii. ep. 28.

Vitruvius mentions a fact which proves Archimedes's knowledge in the doctrine of specific gravity. Hiero, the king, having given a certain quantity of gold wherewith to make a golden crown, and suspecting that the workmen had stolen part of the gold and substituted silver in its stead, he applied to Archimedes to employ his ingenuity in detecting the fraud. Ruminating upon this subject when he was bathing himself, he observed that he dislodged a quantity of water corresponding to the bulk of his own body; therefore, instantly quitting the bath with all the eagerness natural to an inventive mind upon a new discovery, he ran into the street naked, crying, Elezra! Elezra! I have found it out! I have found it out! Then taking one mass of gold and another of silver, each equal in weight to the crown, he carefully observed the quantity of fluid which they alternately displaced, when introduced in the same vessel full of water. Next he ascertained how much water was displaced by the crown when put into the same vessel full of water; and, upon comparing the three quantities together, he ascertained the exact proportions of gold and silver of which the crown was composed.

Archimedes was well acquainted with the mechanical powers. His celebrated saying with regard to the power of the lever has been often repeated,—"Give me a place to stand upon, and I will move the earth." In order to show Hiero the effect of mechanical powers, it is said that, aided by ropes and pulleys, he drew towards him a galley which lay on the shore manned and loaded; but the displays of his mechanical skill mentioned by Marcellus at the siege of Syracuse were long deemed almost incredible, until the after-improvements in mechanics have demonstrated them practicable. He harassed the vessels of the besiegers, both when they approached and kept at a distance from the city. When they approached, he sunk them by means of long and huge beams of wood; or, by means of grappling hooks placed at the extremity of levers, he hoisted up the vessels into the air, and dashed them to pieces either against the walls or the rocks. When the enemy kept at a distance, he employed machines which threw from the walls such a quantity of stones as shattered and destroyed their vessels. In short, his mechanical genius supplied strength and courage to the city, and filled the Romans with astonishment and terror. Until Buffon invented and framed a burning glass, composed of about 400 glass panes, capable of setting fire to wood at the distance of 200 feet, and of melting lead and tin at the distance of 120 feet, and silver at the distance of 50, the account of Archimedes's instrument for burning ships at a great distance by means of the rays of the sun was deemed fabulous and impossible.

But, however eminent for mechanical invention, he was still more eminent for the investigation of abstract truths, and the formation of conclusive demonstrations in pure geometry. Plutarch also mentions that Archimedes himself esteemed mechanical inventions greatly inferior in value to those speculations which convey irresistible conviction to the mind. His geometrical works afford numerous proofs of his success in this field of science. It is reported that he was often so deeply engaged in mathematical speculations, as both to neglect his food and the care of his person; and at the bath he would sometimes draw geometrical figures in the ashes, and sometimes upon his own body when it was anointed, according to the custom of that time. He valued himself so much upon the discovery of the ratio between the sphere and the containing cylinder, that, indifferent to all his other inventions, he ordered his friends to engrave upon his tomb a cylinder containing a sphere, with an inscription explanatory of its nature and use.

It must be extremely painful to every humane mind, but particularly to every lover of philosophic merit, to learn, that when Syracuse was taken by storm, Archimedes, being ignorant of that fact, was run through the body, when engaged in drawing a geometrical figure upon the sand. As Marcellus had given express orders that both his person and his house should be held sacred, this appears to have happened through ignorance, and therefore removes a great part of the odium from the Roman name. This mournful event happened in the 142d Olympiad, or 212 years before the Christian era. Marcellus, in the midst of his triumph, lamented the death of Archimedes, conferred upon him an honourable burial, and took his surviving relations under his protection; but greater honour was conferred upon him when the philosopher of Arpinum, 140 years after, went in search of his long-neglected tomb. Hence, says Cicero, "I diligently sought to discover the sepulchre of Archimedes, which the Syracusans had totally neglected, and suffered to be overgrown with thorns and briers. Recollecting some verses said to be inscribed on the tomb, which mentioned that on the top was placed a sphere with a cylinder, I looked round me upon every object at the Agrigentine gate, the common receptacle of the dead. At last I observed a little column which just rose above the thorns, upon which was placed the figure of a sphere and cylinder. 'This,' said I to the Syracusan nobles who were with me, 'this must, I think, be what I am seeking.' Several persons were immediately employed to clear away the weeds and lay open the spot. As soon as a passage was opened, we drew near, and found on the opposite base the inscription, with nearly half the latter part of the verses worn away. Thus would this most famous, and formerly most learned, city of Greece have remained a stranger to the tomb of one of its most ingenious citizens, had it not been discovered by a man of Arpinum."

Several works of this celebrated mathematician have escaped the wreck of time. In abstract geometry we have a treatise on the Sphere and Cylinder, another on the Dimension of the Circle, or the Proportion between the Diameter and the Circumference; on Obtuse Conoids and Spheroids; on Spiral Lines; and on the Quadrature of the Parabola. Of his mechanics we have a treatise on Equiponderants, or Centres of Gravity; and in hydrostatics, a treatise concerning Bodies floating on Fluids.

The existing works of Archimedes were printed at Basil, in a folio volume, Greek and Latin, in 1544. This is the editio princeps. Another edition was printed at Paris in 1615. The most complete and best is that printed at Oxford in 1792, in a handsome folio volume, superintended by the late Dr Abraham Robertson. There is a French translation by M. Peyrard, of the works of Archimedes: it was published in 1808, in 2 vols. 8vo.