Archimedes of Syracuse — страница 2

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rolled to and fro, and kept swinging, until the mariners were all thrown out, when at length it was dashed against the rocks, or let fall. Archimedes had been persuaded by his friend and relation King Hieron to build such machines:- These machines [Archimedes] had designed and contrived, not as matters of any importance, but as mere amusements in geometry; in compliance with King Hiero's desire and request, some little time before, that he should reduce to practice some part of his admirable speculation in science, and by accommodating the theoretic truth to sensation and ordinary use, bring it more within the appreciation of the people in general. Perhaps it is sad that engines of war were appreciated by the people of this time in a way that theoretical mathematics was not, but

one would have to remark that the world is not a very different place at the end of the second millenium AD. Other inventions of Archimedes such as the compound pulley also brought him great fame among his contemporaries. Again we quote Plutarch:- [Archimedes] had stated [in a letter to King Hieron] that given the force, any given weight might be moved, and even boasted, we are told, relying on the strength of demonstration, that if there were another earth, by going into it he could remove this. Hiero being struck with amazement at this, and entreating him to make good this problem by actual experiment, and show some great weight moved by a small engine, he fixed accordingly upon a ship of burden out of the king's arsenal, which could not be drawn out of the dock without great

labour and many men; and, loading her with many passengers and a full freight, sitting himself the while far off, with no great endeavour, but only holding the head of the pulley in his hand and drawing the cords by degrees, he drew the ship in a straight line, as smoothly and evenly as if she had been in the sea. Yet Archimedes, although he achieved fame by his mechanical inventions, believed that pure mathematics was the only worthy pursuit. Again Plutarch describes beautifully Archimedes attitude, yet we shall see later that Archimedes did in fact use some very practical methods to discover results from pure geometry:- Archimedes possessed so high a spirit, so profound a soul, and such treasures of scientific knowledge, that though these inventions had now obtained him the

renown of more than human sagacity, he yet would not deign to leave behind him any commentary or writing on such subjects; but, repudiating as sordid and ignoble the whole trade of engineering, and every sort of art that lends itself to mere use and profit, he placed his whole affection and ambition in those purer speculations where there can be no reference to the vulgar needs of life; studies, the superiority of which to all others is unquestioned, and in which the only doubt can be whether the beauty and grandeur of the subjects examined, of the precision and cogency of the methods and means of proof, most deserve our admiration. His fascination with geometry is beautifully described by Plutarch:- Oftimes Archimedes' servants got him against his will to the baths, to wash and

anoint him, and yet being there, he would ever be drawing out of the geometrical figures, even in the very embers of the chimney. And while they were anointing of him with oils and sweet savours, with his fingers he drew lines upon his naked body, so far was he taken from himself, and brought into ecstasy or trance, with the delight he had in the study of geometry. The achievements of Archimedes are quite outstanding. He is considered by most historians of mathematics as one of the greatest mathematicians of all time. He perfected a methods of integration which allowed him to find areas, volumes and surface areas of many bodies. Chasles said that Archimedes' work on integration (see):- ... gave birth to the calculus of the infinite conceived and brought to perfection by Kepler,

Cavalieri, Fermat, Leibniz and Newton. Archimedes was able to apply the method of exhaustion, which is the early form of integration, to obtain a whole range of important results and we mention some of these in the descriptions of his works below. Archimedes also gave an accurate approximation to  and showed that he could approximate square roots accurately. He invented a system for expressing large numbers. In mechanics Archimedes discovered fundamental theorems concerning the centre of gravity of plane figures and solids. His most famous theorem gives the weight of a body immersed in a liquid, called Archimedes' principle. The works of Archimedes which have survived are as follows. On plane equilibriums (two books), Quadrature of the parabola, On the sphere and cylinder (two