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Archimedes: Works
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The standard English translation of Archimedes is Thomas L. Health, ed., The Works of Archimedes (1897), which includes a supplement, The Method of Archimedes (1912). For biographical information see E. J. Dijksterhuis, Archimedes (1938; trans. 1956). Archimedes' place in the development of integral calculus is described in Carl B. Boyer, The History of the Calculus and Its Conceptual Development (1949). Works on mathematics for the general reader are Thomas L. Heath, A Manual of Greek Mathematics (1931); Bartel L. van der Waerden, Science Awakening (1950; trans. 1954); and James R. Newman, ed., The World of Mathematics (4 vols., 1956).
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Archimedes was a Greek mathematician that was one of the greatest mathematicians of all time. His ideas and inventions were all ahead of his time, some by centuries. He anticipated many discoveries of modern Science, such as Integral Calculas. Sadly, though, most of his work was lost. He is known for his great inventions, to his great scientific mind, to basically becoming the father of Geometry.
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Archimedes' Cattle Problem Archimedes wrote a letter to the scholars in the Library of Alexandria, who had apparently questioned the importance of his work. He challenges them to count the numbers of cattle in the Herd of the Sun by solving a number of simultaneous Diophantine equations. There is a more difficult version of the problem in which some of the answers are required to be square numbers. This version of the problem was first solved by a computer in 1965, and the answer is a very large number.
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Archimedes' mathematical work exhibits great boldness and originality in thought, as well as extreme rigor. Among his mathematical accomplishments is the computation of pi, which is the ratio of the circumference of a circle to its diameter. His approach consisted of inscribing and circumscribing regular polygons with many sides in and around the circle, and computing the perimeter of these polygons. This provided him with an upper and a lower bound for pi.
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Unlike the Elements of Euclid, the works of Archimedes were not widely known in antiquity. individual works of Archimedes were obviously studied at Alexandria, since Archimedes was often quoted by three eminent mathematicians of Alexandria: Heron, Pappus and Theon.
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[One] of Archimedes' works in mechanics, besides On Floating Bodies mentioned previously, is On the Equilibrium of Planes. From such simple postulates as "Equal weights at equal distances balance," positions of centers of gravity are determined for parabolic segments.
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