one of the most eminent 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 warlike machines, and also for his accurate observation of the heavenly bodies: "Unicus spectator coeli fiderumque, mirabilior tamen inventor ac machinator bellicorum tormentorum," &c. lib. xxiv. 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.

It may perhaps be impossible distinctly to ascertain the different inventions of this great man; but from the following passage, it appears that he formed a glass sphere, or some kind of planetarium, which, with no small degree of accuracy, represented the phenomena of the heavenly bodies. Hence says Claudian

Jupiter, in parvo cum cerneret aethera vitro, Rexit, et ad superos talia dicta delit: Huccine. Huccine mortalis progresse potentia curae? Jam mens in fragilis ludet orbe labor. Jura poli, rerumque fidem, legesque deorum, Ecce Syracusius transfluit arii fenex. Inclusus varvis famulatur spiritus auri, Et verum certis motibus urgat opus. Percurrunt propium menitus signifer annum. Et simulata nova Cynthia menfe redit. Jamque suum volvens audax industria mundum Gaudet, et humana sidera mente regit. Quid falsi insontem tonitru Salmonea miror? Emula naturae parva reperta manus.

"When in a glass's narrow sphere confin'd, Jove saw the fabric of th' Almighty mind; He smil'd, and said, 'Can mortals art alone Our heav'nly labours mimic with their own? The Syracusan's brittle work contains Th' eternal law that through all nature reigns. Fram'd by his art, see stars unnumber'd burn, And in their courses rolling orbs return; His sun, through various signs describe the year, And every month his mimic moons appear. Our rival's laws his little planets bind, And rule their motions by a human mind: Salmoneus could our thunder imitate; But Archimedes can a world create."

In the following lines the same machine is mentioned by Ovid.

Arte Syracosia suspensus in aere clauso, Stat globus, immensi parva figura poli.

OVID, Fast. vi. 277.

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 run into the streets naked, crying, Eugea! Eugea! 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 shew 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 glasses planes, capable of letting 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 the branches of pure geometry. Plutarch also mentions, that Archimedes himself esteemed mechanical invention 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, he, 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 triumphant laurels, 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,"