Archimago

“ Ephesians, vi, 13.
243. that like succeed it may, that like successful adventures may succeed it. The word order is inverted for the sake of the rhyme.
250. to frend, as his friend.
254. An aged Sire, the false enchanter, Archimago, or Hypocrisy, who is supposed to represent Pope Sixtus V or King Philip II of Spain. In general he stands for false religion or the Church of Rome. The character and adventure are taken from Orlando Furioso, ii, 12, in which there is a hypocritical hermit. The Knight at first takes Archimago to be a palmer, and inquires for the foreign news. ”

“ Religious or Spiritual Allegory.—Under this interpretation the Redcross Knight is a personification of Protestant England, or the church militant, while Una represents the true religion of the Reformed Church. On the other hand, Archimago symbolizes the deceptions of the Jesuits and Duessa the false Church of Rome masquerading as true religion. ”

“ In the fight which ensues Archimago is unhorsed and his deception unmasked. The Lion is slain, and Una becomes the captive of Sansloy.
II. The Allegory: 1. Truth finds temporary protection in Reason, or Natural Honor (Lion) , and with its help puts a stop to the Robbing of Churches (Kirkrapine) , which is connived at by Blind Devotion (Corceca) and Secret Sin (Abessa) . Truth is then associated with Hypocrisy under the guise of Holiness, but it is soon unmasked by Lawlessness (Sansloy) , with which Truth is forced into an unnatural alliance. ”

“ The Earth hung over us, flattened beyond the full. The stars blazed to mingle with the Earthlight and illumine these massive crags of the Archimedes walls. But no speck appeared to tell us that the ship was up there.
We were on the curving side of the Archimedes wall which fronted the Mare Imbrium to the North. The plains lay like a great frozen sea, congealed ripples shining in the light of the [210] Earth, with dark patches to mark the hollows. Somewhere down there—six or eight thousand feet below us now, or even more than that, for all I could tell—Miko's encampment lay concealed. ”

“ 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 More efficient devices have superseded it in modern times, but it still excites the admiration of all who examine it, and its effects seem as paradoxical as ever.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. ”

“ 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. ”

“ The young Archimedes seemed to be just as happy as the little tow-headed barbarian. A few minutes ago he had been busy with the theorem of Pythagoras. Now, tooting indefatigably along imaginary rails, he was perfectly content to shuffle backwards and forwards among the flower-beds, between the pillars of the loggia, in and out of the dark tunnels of the laurel tree. [325] The fact that one is going to be Archimedes does not prevent one from being an ordinary cheerful child meanwhile. ”

“ 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. ”

“ 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. ”

“ 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. ”

“ 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." ”

“ Archimedes is said to have requested his friends and relatives to place upon his tomb a representation of a cylinder circumscribing a sphere within it, together with an inscription giving the ratio (3/2) which the cylinder bears to the sphere; from which we may infer that he himself regarded the discovery of this ratio as his greatest achievement. Cicero, when quaestor in Sicily, found the tomb in a neglected state and restored it. In modern times not the slightest trace of it has been found. ”

“ 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. ”

“ 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. ”

“ Book II. is a geometrical tour de force. Here, by the methods of pure geometry, Archimedes investigates the positions of rest and stability of a right segment of a paraboloid of revolution floating with its base upwards or downwards (but completely above or completely below the surface) for a number of cases differing (1) according to the relation between the length of the axis of the paraboloid and the principal parameter of the generating parabola, and (2) according to the specific gravity of the solid in relation to the fluid ”

“ 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 Squaring of the Parabola is one of the geometrical discoveries which has done most honour to Archimedes. It is remarked to have been the first instance of the reducing a curve figure exactly into a square, unless we admit of Hippocrates’s squaring the lunulæ to have been of this sort.
The Burning Glasses, employed by Archimedes to set fire to the Roman fleet at the siege of Syracuse, Kepler, Naudéus, and Descartes have treated as fabulous, though attested by Diodorus Siculus, Lucian, Dion, Zonaras, Galen, Anthemius, Eustathius, Tzetzes, and other eminent authors. ”

“ Almost all that is told of Archimedes reaches us through the accounts by Polybius and Plutarch of the siege of Syracuse by Marcellus. He perished in the sack of that city in 212 B.C., and, as he was then an old man 2 (perhaps 75 years old) , he must have been born about 287 B.C. He was the son of Phidias, an astronomer, and was a friend and kinsman of King Hieron of Syracuse and his son Gelon. He spent some time at Alexandria studying with the successors of Euclid (Euclid who flourished about 300 B.C. was then no longer living) . ”

“ This noted capital was then one of the largest and richest cities of the Grecian world. For three years it held out against the Roman forces. It is said that Archimedes (see p. 213) , the great mathematician, rendered valuable aid to the besieged with curious and powerful engines contrived by his genius. But the city fell at last, and was given over to sack and pillage. Rome was adorned with the rare works of Grecian art—paintings and sculptures—which for centuries had been accumulating in this the oldest and most renowned of the colonies of ancient Hellas. ”

“ 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. ”

“ 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. ”

“ However, the master had the modesty to refuse the dedication of the Temple, and Agrippa was obliged to dedicate it to all the gods in Olympus, in order to take the place of Power, the god of the earth. There was a car of bronze on the top of the Pantheon, on which were placed the statues of Augustus and of Agrippa. On each side of the portico these same statues were placed in another form, and on the pediment of the Temple is still to be read: 'Consecrated by Agrippa.' Augustus gave his name to the age in which he lived because he made that age an epoch of the human mind. ”

“ 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. ”

“ Almost the only incident of his life which is known to us is a conversation between him and that king, who, having asked if there was no easier method of learning the science, is said to have been told by Euclid, that "there was no royal path to geometry." His most famous work is his "Elements of Pure Mathematics," at the present time a manual of instruction and the foundation of all geometrical treatises. Archimedes (287-212 B.C.) was a native of Syracuse, in Sicily, but he traveled to Egypt at an early age, and studied mathematics there in the school of Euclid. ”

“ It was as if he had added his weight to the lever by which Archimedes said he could move the earth. Great stones ground suddenly into place, rollers revolved, and with as harsh a noise as if hundreds of long-disused grindstones had been set in motion the whole mass of crude mechanism moved in bewildering complexity until suddenly the end of the closed tunnel lifted and the first daylight we had seen for hours began streaming in. ”

“ 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. ”