But to borrow Mr. Archimedes exclamation, Eureka!
This has been discredited because it is not mentioned by Polybius, Livy or Plutarch; but it is probable that Archimedes had constructed some such burning instrument, though the connexion of it with the destruction of the Roman fleet is more than doubtful.
Archimedes died at the capture of Syracuse by Marcellus, 212 B.C. In the general massacre which followed the fall of the city, Archimedes, while engaged in drawing a mathematical figure on the sand, was run through the body by a Roman soldier.
- The range and importance of the scientific labours of Archimedes will be best understood from a brief account of those writings which have come down to us; and it need only be added that his greatest work was in geometry, where he so extended the method of exhaustion as originated by Eudoxus, and followed by Euclid, that it became in his hands, though purely geometrical in form, actually equivalent in several cases to integration, as expounded in the first chapters of our text-books on the integral calculus.
Propositions I-II are preliminary, 13-20 contain tangential properties of the curve now known as the spiral of Archimedes, and 21-28 show how to express the area included between any portion of the curve and the radii vectores to its extremities.
This has come down to us through a Latin version of an Arabic manuscript; it cannot, however, have been written by Archimedes in its present form, as his name is quoted in it more than once.
Lastly, Archimedes is credited with the famous Cattle-Problem enunciated in the epigram edited by G.
Lessing' in 1773, which purports to have been sent by Archimedes to the mathematicians at Alexandria in a letter to Eratosthenes.
Of lost works by Archimedes we can identify the following: (I) investigations on polyhedra mentioned by Pappus; (2) Archai, Principles, a book addressed to Zeuxippus and dealing with the naming of numbers on the system explained in the Sand Reckoner; (3) Peri zygon, On balances or levers; (4) Kentrobarika, On centres of gravity; (5) Katoptrika, an optical work from which Theon of Alexandria quotes a remark about refraction; (6) Ephodion, a Method, mentioned by Suidas; (7) Peri sphairopeoia, On Sphere-making, in which Archimedes explained the construction of the sphere which he made to imitate the motions of the sun, the moon and the five planets in the heavens.
- The editio princeps of the works of Archimedes, with the commentary of Eutocius, is that printed at Basel, in 1544, in Greek and Latin, by Hervagius.
Heath (The Works of Archimedes, Cambridge, 1897).
On Archimedes himself, see Plutarch's Life of Marcellus.
Archimedes concluded from his measurements that the sun's diameter was greater than 27' and less than 32'; and even Tycho Brahe was so misled by his measures of the apparent diameters of the sun and moon as to conclude that a total eclipse of the sun was impossible.'
Following Archimedes, Fagnano desired the curve to be engraved on his tombstone.
Archimedes, the famous mathematician, had a celestial globe of glass, in the centre of which was a small terrestrial globe.
Ptolemy's Almagest, the works of Apollonius, Archimedes, Diophantus and portions of the Brahmasiddhanta, were also translated.
Archimedes' problem of dividing a sphere by a plane into two segments having a prescribed ratio,was first expressed as a cubic equation by Al Mahani, and the first solution was given by Abu Gafar al Hazin.
His assault seawards was made mainly on Achradina,1 but the city was defended by a numerous soldiery and by what seems to have been still more formidable, the ingenious contrivances of Archimedes, whose engines dealt havoc among the Roman ships, and frustrated the attack on the fortifications on the northern slopes of Epipolae (Liv.
Archimedes perished in the confusion of the sack while he was calmly pursuing his studies (Liv.
The fundamental principles of hydrostatics were first given by Archimedes in his work H€pi rwv o ovpEvwv, or De its quae vehuntur in humido, about 250 B.C., and were afterwards applied to experiments by Marino Ghetaldi (1566-1627) in his Promotus Archimedes (1603).
As stated first by Archimedes, the principle asserts the obvious fact that a body displaces its own volume of water; and he utilized it in the problem of the determination of the adulteration of the crown of Hiero.
As the molten metal is run in, the upward thrust on the outside mould, when the level has reached PP', is the weight of metal in the volume generated by the revolution of APQ; and this, by a theorem of Archimedes, has the same volume as the cone ORR', or rya, where y is the depth of metal, the horizontal sections being equal so long as y is less than the radius of the outside FIG.
Like another Archimedes, he requested that the logarithmic spiral should be engraven on his tombstone, with these words, Eadem mutata resurgo.
If, therefore, the walls of the enclosure held the gas that is directly in contact with them, this equilibrium would be the actual state of affairs; and it would follow from the principle of Archimedes that, when extraneous forces such as gravity are not considered, the gas would exert no resultant force on any body immersed in it.
The founder of the mathematical school was the celebrated Euclid (Eucleides); among its scholars were Archimedes; Apollonius of Perga, author of a treatise on Conic Sections; Eratosthenes, to whom we owe the first measurement of the earth; and Hipparchus, the founder of the epicyclical theory of the heavens, afterwards called the Ptolemaic system, from its most famous expositor, Claudius Ptolemaeus.
At Pavia in 1494 we find him taking up literary and grammatical studies, both in Latin and the vernacular; the former, no doubt, in order the more easily to read those among the ancients who had laboured in the fields that were his own, as Euclid, Galen, Celsus, Ptolemy, Pliny, Vitruvius and, above all, Archimedes; the latter with a growing hope of some day getting into proper form and order the mass of materials he was daily accumulating for treatises on all his manifold subjects of enquiry.