This wonderful genius was of royal descent, and born at Syracuse about B.C. 287. He was a relative of king Hiero, who held him in the highest esteem and favor, though he does not appear to have held any public office, preferring to devote himself entirely to science. Such was his enthusiasm, that he appears at times to have been so completely absorbed in contemplation and calculations, as to be totally unconscious of what was passing around him. We cannot fully estimate his services to mathematics, for want of an acquaintance with the previous state of science; still we know that he enriched it with discoveries of the highest importance, upon which the moderns have founded their admeasurements of curvilinear surfaces and solids. Euclid, in his elements, considers only the relations of some of these magnitudes to each other, but does not compare them with surfaces and solids bounded by straight lines. Archimedes developed the proportions necessary for effecting this comparison, in his treatises on the sphere and cylinder, the spheroid and conoid, and in his work on the measure of the circle. He rose to still more abstruse considerations in his treatise on the spiral. Archimedes is also the only one of the ancients who has left us anything satisfactory on the theory of mechanics and hydrostatics. He first taught the principle "that a body immersed in a fluid, loses as much in weight, as the weight of an equal volume of the fluid." He discovered this while bathing, which is said to have caused him so much joy that he ran home from the bath undressed, exclaiming, "I have found it; I have found it!" By means of this principle, he determined how much alloy a goldsmith had added to a crown which king Hiero had ordered of pure gold. Archimedes had a profound knowledge of mechanics, and in a moment of enthusiasm, with which the extraordinary performances of his machines had inspired him, he exclaimed that he "could move the earth with ease, by means of his machines placed on a fixed point near it." He was the inventor of the compound pulley, and probably of the endless screw which bears his name. He invented many surprising engines and machines. Some suppose that he visited Egypt, and raised the sites of the towns and villages of Egypt, and begun those mounds of earth by means of which communication was kept up from town to town, during the inundations of the Nile. When Marcellus, the Roman consul, besieged Syracuse, he devoted all his talents to the defense of his native country. He constructed machines which suddenly raised up in the air the ships of the enemy in the bay before the city, and then let them fall with such violence into the water that they sunk; he also set them on fire with his burning glasses. Polybius, Livy, and Plutarch speak in detail, with wonder and admiration, of the machines with which he repelled the attacks of the Romans. When the town was taken and given up to pillage, the Roman general gave strict orders to his soldiers not to hurt Archimedes, and even offered a reward to him who should bring him alive and safe to his presence. All these precautions proved useless, for the philosopher was so deeply engaged at the time in solving a problem, that he was even ignorant that the enemy were in possession of the city, and when a soldier entered his apartment, and commanded him to follow him, he exclaimed, according to some, "Disturb not my circle!" and to others, he begged the soldier not to "kill him till he had solved his problem"; but the rough warrior, ignorant of the august person before him, little heeded his request, and struck him down. This happened B.C. 212, so that Archimedes, at his death, must have been about 75 years old. Marcellus raised a monument over him, and placed upon it a cylinder and a sphere, thereby to immortalize his discovery of their mutual relations, on which he set a particular value; but it remained long neglected and unknown, till Cicero, during his questorship of Sicily, found it near one of the gates of Syracuse, and had it repaired. The story of his burning glasses had always appeared fabulous to some of the moderns, till the experiments of Buffon demonstrated its truth and practicability. These celebrated glasses are supposed to have been reflectors made of metal, and capable of producing their effect at the distance of a bow-shot.