Archimedes' screw, a simple mechanical device believed to have been invented by Archimedes in the 3d cent. B.C. It consists of a cylinder inside of which a continuous screw, extending the length of the cylinder, forms a spiral chamber. By placing the lower end in water and revolving the screw, water is raised to the top. The principle is applied in machines used for drainage and irrigation, and also in some types of high-speed tools. It can also be applied for handling light, loose materials such as grain, sand, and ashes.

Archimedes' principle, principle that states that a body immersed in a fluid is buoyed up by a force equal to the weight of the displaced fluid. The principle applies to both floating and submerged bodies and to all fluids, i.e., liquids and gases. It explains not only the buoyancy of ships and other vessels in water but also the rise of a balloon in the air and the apparent loss of weight of objects underwater. In determining whether a given body will float in a given fluid, both weight and volume must be considered; that is, the relative density, or weight per unit of volume, of the body compared to the fluid determines the buoyant force. If the body is less dense than the fluid, it will float or, in the case of a balloon, it will rise. If the body is denser than the fluid, it will sink. Relative density also determines the proportion of a floating body that will be submerged in a fluid. If the body is two thirds as dense as the fluid, then two thirds of its volume will be submerged, displacing in the process a volume of fluid whose weight is equal to the entire weight of the body. In the case of a submerged body, the apparent weight of the body is equal to its weight in air less the weight of an equal volume of fluid. The fluid most often encountered in applications of Archimedes' principle is water, and the specific gravity of a substance is a convenient measure of its relative density compared to water. In calculating the buoyant force on a body, however, one must also take into account the shape and position of the body. A steel rowboat placed on end into the water will sink because the density of steel is much greater than that of water. However, in its normal, keel-down position, the effective volume of the boat includes all the air inside it, so that its average density is then less than that of water, and as a result it will float.

Archimedes, 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.

Law of buoyancy, discovered by Archimedes, which states that any object that is completely or partially submerged in a fluid at rest is acted on by an upward, or buoyant, force. The magnitude of this force is equal to the weight of the fluid displaced by the object. The volume of fluid displaced is equal to the volume of the portion of the object submerged.

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(born circa 290–280 BC, Syracuse, Sicily—died 212/211 BC, Syracuse) Legendary Greek inventor and mathematician. His principal discoveries were the Archimedes screw, an ingenious device for raising water, and the hydrostatic principle, or Archimedes' principle. His main interests were optics, mechanics, pure mathematics, and astronomy. Archimedes' mathematical proofs show both boldly original thought and a rigour meeting the highest standards of contemporary geometry. His approximation of π was not improved on until after the Middle Ages, and translations of his works were important influences on 9th-century Arab and 16th- and 17th-century European mathematicians. In his native city, Syracuse, he was known as a genius at devising siege and countersiege weapons. He was killed by a Roman soldier during the storming of the city.

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