Which Greek mathematician, physicist, engineer, inventor, and astronomer used the method of exhaustion to calculate the area under a parabola, and provided formulas for the volumes of surfaces of revolution and a system for expressing very large numbers?
History of mathematical notation are Hydrostatics, Optics, Navigation, &c. Archimedes is generally considered to be the greatest mathematician of antiquity and one of the greatest of all time. He used the method of exhaustion to calculate the area under the arc of a parabola with the summation of an infinite series, and gave a remarkably accurate approximation of pi. He also defined the spiral bearing his name, formulae for the volumes of surfaces of revolution and an ingenious system for expressing very large numbers. In the historical development of geometry, the steps in the abstraction of geometry were made by the ancient Greeks. Euclid's
Method of exhaustion well he understood it. The theory was made rigorous a few decades later by Eudoxus of Cnidus, who used it to calculate areas and volumes. It was later reinvented in China by Liu Hui in the 3rd century AD in order to find the area of a circle. The first use of the term was in 1647 by Gregory of Saint Vincent in "Opus geometricum quadraturae circuli et sectionum". The method of exhaustion is seen as a precursor to the methods of calculus. The development of analytical geometry and rigorous integral calculus in the 17th-19th centuries subsumed the method of