Archimedes was born B.C. 287, and is said to have been related by blood to Hiero, king of Syracuse. He was too late to associate with Euclid, but found a friend and genial companion in Conon, another distinguished mathematician of that age. In his researches Archimedes used "his beloved Doric dialect," and contributed much to the improvement of mathematical science. His first discoveries related to the area of the parabola, the surface and solidity of the sphere and cylinder, the properties of spheroids, and of that spiral which is called indifferently the spiral of Conon or of Archimedes. The speculations respecting the sphere and cylinder appear to have interested this great man the most, for he wished to have his grave marked by these solids, and was the first mathematician who caused his scientific discoveries to be inscribed on his tomb. Of his astronomical studies, none have reached our times, excepting the method of determining the sun's apparent diameter. Cicero speaks of an orrery, as it would be called in modern times, made by Archimedes, and exhibiting the motion of the sun, the moon, and the planets; which he uses as an argument against those who deny a Providence. "Shall we," says he, "attribute more intelligence to Archimedes for making the imitation, than to nature for framing the original?" Perhaps the most remarkable of his discoveries were those he made in mechanics, and their adaptation by him to practical use. The lever, the wheel and axle, the polyspact or pulley, the wedge, and the screw were known to him. He seems to have turned much of his attention to the construction of powerful machines, and boasted of the unlimited extent of his art in the well-known expression, "Give me a spot to stand on, and I will move the earth." He is said to have enabled Hiero, through a mechanical contrivance, to push a large ship into the sea, by his individual strength. His application was so intense that he required to be reminded of the common duties of eating and drinking by those about him; and while his servants were placing him in his bath, he would still continue drawing mathematical diagrams with any materials within his reach. "So that," according to Plutarch, "this abstraction made people say, and not unreasonably, that he was accompanied by an invisible siren, to whose song he was listening."