# Archimedes the areas andvolumes of curved solid

### Archimedes the areas andvolumes of curved solid

Archimedes (287-212 BC), preeminent Greekmathematician and inventor, who wrote important workson plane and solid geometry, arithmetic, and mechanics.Archimedes was born in Syracuse, Sicily, and educated inAlexandria, Egypt. In pure mathematics he anticipatedmany of the discoveries of modern science, such as theintegral calculus, through his studies of the areas andvolumes of curved solid figures and the areas of planefigures. He also proved that the volume of a sphere istwo-thirds the volume of a cylinder that circumscribes thesphere.

In mechanics, Archimedes defined the principle ofthe lever and is credited with inventing the compoundpulley. During his stay in Egypt he invented the hydraulicscrew for raising water from a lower to a higher level. He isbest known for discovering the law of hydrostatics, oftencalled Archimedes’ principle, which states that a bodyimmersed in fluid loses weight equal to the weight of theamount of fluid it displaces. This discovery is said to havebeen made as Archimedes stepped into his bath andperceived the displaced water overflowing, and afterviewing that had ran outside into the streets nakedscreaming “Eureka!(I found it!)” Archimedes spent themajor part of his life in Sicily, in and around Syracuse. Hedid not hold any public office but devoted his entire lifetimeto research and experiment.

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During the Roman conquest ofSicily, however, he placed his gifts at the disposal of thestate, and several of his mechanical devices were employedin the defense of Syracuse. Among the war machinesattributed to him are the catapult and-perhaps legendary-amirror system for focusing the sun’s rays on the invaders’boats and igniting them. After the capture of Syracuseduring the Second Punic War, Archimedes was killed by aRoman soldier who found him drawing a mathematicaldiagram in the sand. It is said that Archimedes was soabsorbed in calculation that he offended the intruder merelyby remarking, “Do not disturb my diagrams.” Several of hisworks on mathematics and mechanics survive, includingFloating Bodies, The Sand Reckoner, Measurement of theCircle, Spirals, and Sphere and Cylinder.

They all exhibitthe rigor and imaginativeness of his mathematical thinking.Category: History