In consequence of the brave resistance made by the Syracusans, Marcellus converted the siege into a bloc kade, and waited a favourable opportunity for taking the city by surprise. The success of the besieged lulled them into a fatal security. During the celebration of the festival of Diana, the centinels were not posted on the towers ; and the Romans taking advantage of the blind confidence of the enemy, scaled the walls, and carried their victorious arms into the heart of the city. Nrchimedes was engaged in his favourite studies, when a Roman soldier entered his apartment. Marcellus had given strict orders that Archimedes should he spared ; but, either from the soldier's ignorance of this injunc tion, or from Archimedes's refusing to accompany him to Marcellus, he plunged his sword into the heart of the philosopher. When the news of his death reached Marcellus, he exhibited the greatest affliction at the loss of this illustrious character, and testified the sin ccrity of his feelings, by loading with favours the rela tions of Archimedes, and by fulfilling the desire of the philosopher, that a sphere, inscribed in a cylinder, should be engraved upon his tomb. About 140 years alter the death of Archimedes, Cicero, when Questor in Sicily, discovered this tomb, and ordered it to be cleared from the thorns and brambles among which it was concealed.
The discoveries of Archimedes in geometry, though almost incorporated with the elements of that science, are perhaps the most brilliant that have been made by the ancients. In his two books on the sphere and cy linder, he has demonstrated this beautiful theorem, that the surface, as well as the solidity of any sphere, is equal to two-thirds of its circumscribing cylinder; and that the surface of each cylindrical segment, comprehended between planes perpendicular to the axis, is equal to the superficies of the corresponding spherical segment.
In his treatise on the mensuration of the circle, Ar chimedes has shewn, that the ratio of the diameter, to the circumference of the circle, is as 7 to 22; a result which he obtained by taking an arithmetical mean be tween the perimeters of the inscribed and circumscrib ed polygons.
In his work on conoids and spheroids he has given many profound and ingenious views, respecting the. mutual relation of these solids, and their relation to cy linders and cones of the same base and altitude. He discovered that the solidity of the parabolic conoid is one half of that of the circumscribed cylinder, or laic of a cone of the same base and vertex ; and that the area of the parabola is .4 ds of that of the inscribed tri angle, or 5ds of that of the circumscribed parallelo gram.
Though the spiral was invented by Conon, the friend of Archimedes, yet we are indebted solely to the Sy racusan philosopher for a knowledge of its properties.
Besides pointing out the method of drawing tangents to their curve, he has shewn that any sector of the spiral is Id of the circular sector which encloses it, and, consequently, that a spiral, which has made one revolu tion, is equal to id of the circle in which it is compre hended.
The 'discoveries of Archimedes, in the science of me chanics, were scarcely less important than those which he made in geometry. In his two books, entitled .De .E.quiponderantibus, or he has demonstrated the fundamental property of the lever ; namely, that a balance, with inequal arms, will be in equilibrio if the two weights in its opposite scales, are reciprocally pro portional to the arms of the balance. By considering the construction of his balance, which moved upon a ful.• cruet, he perceived that the fulcrum sustained the same pressure as if both the weights had directly rested upon it ; and he discovered, that in every single body, and combination of bodies, there must be a centre of firessure or gravity. Pursuing this happy thought, he pointed out the method of finding the centre of gravity of plane surfaces, whether they are limited by a parallelogram, a triangle, a trapezium, or a parabola.
The treatise of Archimedes, rigs Zixspayeev, or " De its qux vehuntur influido," contains the general hydro statical principles on which that interesting science has been founded. He sheaved, that, when any fluid mass is in equilibrium, each particle is equally pressed in every direction, and he investigated the conditions of equili brium of a solid body floating in a fluid.
Every person is acquainted with the process by which Archimedes detected the impurity of King 11.ero's crown, and with the ostentatious declaration, tnat a rest ing place only was wanting, to enable him to move the earth from its place. Many other contrivances have been ascribed to Archimedes, but without the authority of authentic history. The screw for raising water, which bears his name ; the system of pulleys ; the end less screw ; and several combinations of machinery for raising weights, and discharging stones and arrows, have been ranked among his inventions.
The works of Archimedes, as arranged by Torelli, are, I. De Planorum Equilibriis, cum Comment. Eutoc. As calonitx. 2. Quadratura Paraboles. 3. De Planorum Equilibriis. cum Comm. Eutoc. Ascalon. 4. De Spluer. et. Cylindra, lib. prim. cum Comm. Eutoc. Ascalon. 5. De Sph,er. et Cylindro. lib. sec. cum. Comm. Eutoc. Ascalon. 6. Circuli Dimensio, cum Comm. Eutoc. As calon. 7. De Hrlicibus. 8. De Conoidibus et Spheroidi bus, cum Torelli Comment in Prop. 12. 9. Arenariu.s. 10. De its in Humid° Vehuntur, lib prim. 11. De its cute in Humid° Vehuntur, lib. sec. 12. Lemmata. 13. Oftera Mechanica, ut cujusque mentio ab antiquis scrip toribus facta est.