ARCHIMEDES of Syracuse was the son of Pheidias the astronomer, and on intimate terms with, if not related to, King Hieron and his son Gelon. He spent some of his life in Alexandria, and was friendly with Conon of Samos and Eratosthenes; then returned to Syracuse for a life devoted to mathematical research. He perished in 212 B.C. (at age 75, according to Tzetzes) in the sack of Syracuse.
Stories of other details of his life, culled from many sources, are somewhat dubious. No authenticated picture remains, in spite of three (totally different) purported portraitures in classical works of the last century. The only contemporary biography is not extant.
Tales of his preoccupied abstraction - drawing diagrams in ashes, or in oil when anointing himself, and forgetfulness of food - remind us irresistibly of Newton's going out in a fit of absentmindedness without his trousers. He died as he had lived, deep in mathematical contemplation. Several authors give variously garbled accounts, the most picturesque being that, though Marcellus the Roman commander wished him to be spared, a common soldier, enraged by the great man's request to "Stand away, fellow, from my diagram," dispatched him. As he had asked, his discovery of the surfaces of the sphere and cylinder was depicted on his tombstone, which was later found in a dilapidated state and restored by Cicero when quaestor in Sicily.
His mechanical achievements include the water-screw, invented in Egypt for irrigational purposes and used for pumping from mines or ship-holds, and a very accurate model of the planetary system demonstrating eclipses. Some of his inventions were very effective during the siege of Syracuse - catapults of variable range and other machines discharging showers of missiles, and crane-like grappling contrivances which seized the prows of ships and thus played "pitch-and-toss" with them. The Romans were in such abject terror that "if they did but see a piece of rope or wood projecting above the wall, they would cry 'there it is again,' declaring that Archimedes was setting some engine in motion against them, and would turn their backs and run away, insomuch that Marcellus desisted from all conflicts and assaults, putting all his hope in a long siege" (Plutarch). The story that he fired the Roman ships by use of concave burning-glasses and mirrors is very doubtful, being first recorded in Lucian, 300 years later.
When Hieron asked for a practical demonstration of a great weight moved by a small force, in connection with his famous utterance "" (Give me a place to stand on, and I can move the Earth), he drew a loaded ship safely and smoothly along with a compound pulley or, according to another account, a helix, a machine with a cogwheel with oblique teeth. Hieron thereupon declared that "from that day forth Archimedes was to be believed in everything that he might say."
Born just before the death of Euclid and 30 years senior to Apollonius of Perga, the "Great Geometer" and last of the three great mathematicians of antiquity, he wrote works with a larger proportion of originality. "It is not possible to find in geometry more difficult and troublesome questions or more simple and lucid explanations." Like most of the ancients, he left little clue as to his method of discovery. He seems "as it were of set purpose to have covered up the traces of his investigation as if he had grudged posterity the secret of his method of inquiry while he wished to extort from them assent to his results" (Wallis). But a manuscript of the "Methods of mechanical theorems," discovered in 1906 in Constantinople and addressed to Eratosthenes, lifts the veil a little.
Other works entitled "On the equilibrium of planes," "On the quadrature of the parabola," "On conoids and spheroids," "On floating bodies," "On the measurement of a circle," "The Sand-reckoner" and a collection of lemmas indirectly due to him are still extant. Lost works are thought to refer to polyhedra, balances and levers, centres of gravity, the calendar, optics, water-clocks and a work entitled "On sphere-making." Arabian writers attribute other works to him.
His main achievements were: quadrature of the parabola, finding surfaces and volumes of spheres, segments of spheres and segments of quadrics of revolution, the approximation , the invention of a number-scale up to 10 to the power 8.1010 (in the Sand-reckoner), geometrical solution of some cubic equations, a method of finding square roots of non-squares, and the whole science of hydrostatics even up to determining the positions of equilibrium and stability of floating segments of a paraboloid. He was also much occupied by astronomy - Livy calls him "unicus spectator caeli siderumque." He is further credited with authorship of the "cattle-problem," which involves eight unknowns and the solution of which has 12 or 206545 digits according to how an ambiguous statement is interpreted. The "loculus Archimedius," a puzzle of 14 shapes fitting together to form a square, is now thought due to him, although the phrase "" was simply a proverbial expression for something very difficult.
He regarded his ingenious mechanical investions simply as "diversions of geometry at play" and "he possessed so high a spirit, so profound a soul, and such treasures of scientific knowledge that, though these inventions had obtained for him the renown of more than human sagacity, he yet would not deign to leave behind him any written work on such subjects, but, regarding as ignoble and sordid the business of mechanics and every sort of art which is directed to use and profit, he placed his whole ambition in those speculations in whose beauty and subtlety there is no admixture of the common needs of life" (Plutarch).
Reproduced from Eureka 27 pages 32-34.
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Errata: the fourth word of "" should start with sigma rather than omicron, "investions" should read "inventions".
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