### Topic Page: Archimedes

**Archimedes**from

*Philip's Encyclopedia*

Greek mathematician and engineer. He developed a method for expressing large numbers and made outstanding discoveries about the determination of areas and volumes, which led to an accurate method of measuring π (pi). In his work On Floating Bodies he stated Archimedes' Principle. He also invented the Archimedes' screw.

**Archimedes**

*The Columbia Encyclopedia*

(ärkĭmē'dēz), 287–212 B.C., Greek mathematician, physicist, and inventor. He is famous for his work in geometry (on the circle, sphere, cylinder, and parabola), physics, mechanics, and hydrostatics. He lived most of his life in his native Syracuse, where he was on intimate terms with the royal family. Few facts of his life are known, but tradition has made at least two stories famous. In one story, he was asked by Hiero II to determine whether a crown was pure gold or was alloyed with silver. Archimedes was perplexed, until one day, observing the overflow of water in his bath, he suddenly realized that since gold is more dense (i.e., has more weight per volume) than silver, a given weight of gold represents a smaller volume than an equal weight of silver and that a given weight of gold would therefore displace less water than an equal weight of silver. Delighted at his discovery, he ran home without his clothes, shouting "Eureka," which means "I have found it." He found that Hiero's crown displaced more water than an equal weight of gold, thus showing that the crown had been alloyed with silver (or another metal less dense than gold). In the other story he is said to have told Hiero, in illustration of the principle of the lever, "Give me a place to stand, and I will move the world." He invented machines of war (Second Punic War) so ingenious that the besieging armies of Marcus Claudius Marcellus were held off from Syracuse for three years. When the city was taken, the general gave orders to spare the scientist, but Archimedes was killed. Nine of Archimedes' treatises, which demonstrate his discoveries in mathematics and in floating bodies, are extant. They are On the Sphere and Cylinder, On the Measurement of the Circle, On the Equilibrium of Planes, On Conoids and Spheroids, On Spirals, On the Quadrature of the Parabola, Arenarius [or sand-reckoner], On Floating Bodies, and On the Method of Mechanical Theorems. Archimedes' many contributions to mathematics and mechanics include calculating the value of π, devising a mathematical exponential system to express extremely large numbers (he said he could numerically represent the grains of sand that would be needed to fill the universe), developing Archimedes' principle, and inventing Archimedes' screw.

- See studies by T. L. Heath (1953) and E. J. Dijksterhuis (1956).

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