Archimedes

“ So that while it is true that Archimedes could move the world, the space through which he could have moved it, during his whole life, from infancy to old age, is so small that even if multiplied two hundred million times it could not be measured by even the most delicate of our modern measuring instruments. ”

“ Imprudent and excessive was the fervour of Archimedes, a lover of geometry, who would not declare his name, nor lift his head from the diagram he had drawn, by which he might have prolonged his life, but thinking more of study than of life dyed with his life-blood the figure he was studying. ”

“ Maxwell and La Grange had taught me that Archimedes, Galileo, Newton, Carnot, Helmholtz, and other great investigators had made the dynamical sciences; and from that time on these sciences like monuments recalled to my mind the names of the men who made them. I never saw a man handling a crowbar without remembering that it was the historic lever which in the philosophy of Archimedes served as the earliest foundation for the science of statics. ”

“ THE WORKS OF ARCHIMEDES.
The range of Archimedes’s writings will be gathered from the list of his various treatises. An extraordinarily large proportion of their contents represents entirely new discoveries of his own. He was no compiler or writer of text-books, and in this respect he differs from Euclid and Apollonius, whose work largely consisted in systematising and generalising the methods used and the results obtained by earlier geometers. There is in Archimedes no mere working-up of existing material; his objective is always something new, some definite addition to the sum of knowledge. ”

“ Archimedes (a ̇r-ki-mē ́dēz) , a celebrated ancient Greek physicist and geometrician, born at Syracuse, in Sicily, about 287 B.C. He devoted himself entirely to science, and enriched mathematics with discoveries of the highest importance, upon which the moderns have founded their admeasurements of curvilinear surfaces and solids. Archimedes is the only one among the ancients who has left us anything satisfactory on the theory of mechanics and on hydrostatics. ”

“ Beyond the above particulars of the life of Archimedes, we have nothing but a number of stories which, if perhaps not literally accurate, yet help us to a conception of the personality of the man which we would not willingly have altered. ”

“ He was thinking by himself, and even seriously racking his brain to find a direction for this single force four times multiplied, with which he did not doubt, as with the lever for which Archimedes sought, they should succeed in moving the world, when someone tapped gently at his door. ”

“ Yet 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 ”

“ The Romans finally took the city by surprise. Tradition tells that, as the assailants were rushing through the streets, with death in their hands, they found Archimedes sitting in the public square, with a number of geometrical figures drawn before him in the sand, which he was studying in oblivion of the tumult of war around. As a Roman soldier rushed upon him sword in hand, he called out to the rude warrior not to spoil the circle. ”

“ The ingenious mechanism excited the wonder of the contemporaries of Archimedes, as well it might. More efficient devices have superseded it in modern times, but it still excites the admiration of all who examine it, and its effects seem as paradoxical as ever.
Some other of the mechanisms of Archimedes have been made known to successive generations of readers through the pages of Polybius and Plutarch. These are the devices through which Archimedes aided King Hiero to ward off the attacks of the Roman general Marcellus, who in the course of the second Punic war laid siege to Syracuse. ”

“ My only wish is to have the opportunity of cultivating some intercourse with the hands beyond the mere ‘cash nexus.’ But it might be the point Archimedes sought from which to move the earth, to judge by the importance attached to it by some of our manufacturers, who shake their heads and look grave as soon as I name the one or two experiments that I should like to try. ”

“ Among the great prelates, who was there to stand in the place of those men whose achievements had glorified the human race? Who was to succeed to Archimedes, Hipparchus, Euclid, Herophilus, Eratosthenes? who to Plato and Aristotle? The quackeries of miracle-cure, shrine-cure, relic-cure, were destined to eclipse the genius of Hippocrates, and nearly two thousand years to intervene between Archimedes and Newton, nearly seventeen hundred between Hipparchus and Kepler. ”

“ But we must leave Archimedes for a man not perhaps so well known, but to whom we owe as much as to the great Syracusan—Hipparchus the astronomer. To his case much which I have just said applies. In him astronomic science seemed to awaken suddenly to a true inductive method, and after him to fall into its old slumber for 300 years. ”

“ Can we infer, however, from these experiments of Buffon, that Archimedes actually destroyed the Roman galleys? We think not; considering the silence of the Roman writers on the subject, and the progress of science in the time of Buffon, with reference to its discoveries in the time of the Siege of Syracuse by Marcellus. Whether this mirror existed or not, however, Archimedes must be admitted to be one of the greatest geniuses the World of Science ever produced. ”

“ Archimedes, however, in writing to king Hiero, whose friend and near relation he was, had stated, 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. ”

“ If any man could have discovered the utmost powers of the cannon, in all its various forms and have given such a secret to the Romans, with what rapidity would they have conquered every country and have vanquished every army, and what reward could have been great enough for such a service! Archimedes indeed, although he had greatly damaged the Romans in the siege of Syra- cuse, nevertheless did not fail of being offered great rewards from these very Romans; and when Syracuse was taken, diligent search was made for Archimedes; ”

“ On the contrary, the daily use of very simple instruments, of the balance for example, reveals to us, on the subject of the equilibrium of heavy objects, some rules of which the truth and the generality would not be able to be made into the object of any doubt. Following the method of which his master Euclid has made usage in the Elements, Archimedes will require of whomever wants to follow his teaching from him to agree with the certitude of these few propositions, from which he will deduce all of his theory. ”

“ On the contrary, the iconography and hagiology of Scientism are as copious as they are mostly squalid. But no student of science has yet been taught that specific gravity consists in the belief that Archimedes jumped out of his bath and ran naked through the streets of Syracuse shouting Eureka, Eureka, or that the law of inverse squares must be discarded if anyone can prove that Newton was never in an orchard in his life. ”

“ Famed as the first great geometrician, Archimedes is best known for his principle upon which all ship construction is based—the buoyant force exerted by a liquid is equal to the weight of the displaced liquid. In other words, a shaped object of metal, such as a ship, will float if it displaces a sufficient quantity of water. King Hiero of Syracuse, a relative of Archimedes, gave him the problem of determining whether or not a new crown he had received was made of pure gold, as ordered, or whether the gold had been mixed with silver. ”

“ As otherwise quoted, the remark of Archimedes was that, had he a place on which to stand, he could move the world, a remark which even more than the other illustrates the full and acute appreciation of the laws of motion; since, as we have already pointed out, action and reaction being equal, the most infinitesimal push must be considered as disturbing even the largest body. ”

“ We think of such conceptual images as ensuing from quite unprejudiced research and, subject to certain conditions, definitively valid. But a first-rate scientist of the time of Archimedes would have declared himself, after a thorough study of our modern theoretical physics, quite unable to comprehend how anyone could assert such arbitrary, grotesque and involved notions to be Science, still less how they could be claimed as necessary consequences from actual facts. ”

“ But, perhaps, a greater even than Euclid was Archimedes, born 287 B.C., who wrote on the sphere and cylinder, which terminate in the discovery that the solidity and surface of a sphere are respectively two thirds of the solidity and surface of the circumscribing cylinder. He also wrote on conoids and spheroids. "The properties of the spiral, and the quadrature of the parabola were added to ancient geometry by Archimedes, the last being a great step in the progress of the science, since it was the first curvilineal space legitimately squared." ”

“ When Archimedes was 73 years old and respected throughout the civilized world for his work in mathematics and science, the Roman invader Marcellus lay siege to Syracuse. At the beginning of the two long years of struggle, Archimedes put aside his theoretical work and with the vigor of a youth helped to defend the city, inventing numerous engines of war for the purpose. In this he was the real pioneer of the scientists of our own day who perfected in wartime the atomic bomb, radar and other devices. ”

“ Archimedes had stirred the intellectual world, but had not put it in progressive motion: the science of Mechanics stopped where he left it. And though, in some objects, as in Harmonics, much was written, the works thus produced consisted of deductions from the fundamental principles, by means of arithmetical calculations; occasionally modified, indeed, by reference to the pleasures which music, as an art, affords, but not enriched by any new scientific truths. ”

“ From these accounts, we may conclude that the mirrors of Archimedes and Buffon were not very different either in their construction or effects. No question, therefore, could remain of the latter having revived one of the most beautiful inventions of former times, were there not one circumstance which still renders the antiquity of it doubtful: the writers contemporary with Archimedes, or nearest his time, make no mention of these mirrors. Livy, who is so fond of the marvellous, and Polybius, whose accuracy so great an invention could scarcely have escaped, are altogether silent on the subject. ”

“ And it is to be feared that few who are not experts in the history of mathematics have any acquaintance with the details of the original discoveries in mathematics of the greatest mathematician of antiquity, perhaps the greatest mathematical genius that the world has ever seen.
History and tradition know Archimedes almost exclusively as the inventor of a number of ingenious mechanical appliances, things which naturally appeal more to the popular imagination than the subtleties of pure mathematics. ”

“ From their profound researches touching the laws of equilibrium, the ancients have left us monuments little numerous, it is true, but worth an eternal admiration. Of these monuments the most beautiful, without contradiction, are the book consecrated by Aristotle to the questions of mechanics and the treatises of Archimedes. ”

“ Seven hundred pounds, however, seems beyond the ability of any such machines as this; but from his higher walls Archimedes could, of course, have rolled such stones down on the decks of the ships below. And if he were throwing other stones or leaden balls to a greater distance with his Onagers, it may well be that Plutarch or Livy did not take very accurate account of the particular engine which threw one stone or another.
Archimedes was killed by a Roman soldier, to the great grief of Marcellus, when the Romans finally took Syracuse. ”

“ We dare not stop to consider Archimedes, lest we stray too far from our subject, but this marvelous man of ancient times, the Benjamin Franklin of his day, seems to have had a hand in almost every sort of mechanical and scientific research, from discovering the principle of specific gravity, in order to checkmate a dishonest goldsmith, to destroying Roman war-ships by means of his scientific "engines." ”

“ At first we should not encumber our pupils with accurate demonstration. The application of mathematics to mechanics is undoubtedly of the highest use, and has opened a source of ingenious and important inquiry. Archimedes, the greatest name amongst mechanic philosophers, scorned the mere practical application of his sublime discoveries, and at the moment when the most stupendous effects were producing by his engines, he was so deeply absorbed in abstract speculation as to be insensible to the fear of death. ”

“ Our author feels himself reduced to the dilemma of the famous Archimedes in this case, though for a very different reason, and exclaims violently for the Δος που στω, not because he has no ground to stand upon, but because he has too much—because puzzled by the variety, he feels an incapacity to make a selection. ”