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Aristotle and Mathematics

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A. Hippocrates of Chios ( B.C.)

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1.Orderly Arrangement of Theorems 2.Indirect Method of Proof 3.Author of a Geometry Text 4.Calculation of Curvilinear Areas Mathematical Thought From Ancient to Modern Times, Morris Kline, Oxford University Press, New York, 1972, p.41

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B.Eudoxus of Cnidus ( B.C.)

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1.Use of Explicit Axioms 2.Method of Exhaustion

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C. Aristotle ( B.C.)

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1.Member of Platos Academy 2.Founder of the Lyceum

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C. Aristotle ( B.C.) 3.Laws of Logic 4.Deduction and Induction 5.Concept of a Specific Science 6.Axiomatic Method 7.Nature of Definitions 8.Undefined Terms

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D.Euclid (c B.C.)

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1.Axioms 2.Definitions 3.Deductive Approach 4.Conic Sections

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E. Archimedes ( B.C.)

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1.Calculation of Areas and Volumes 2.Excellent Estimate of Pi 3.Law of Levers 4.Hydrostatics

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F. Apollonius ( B.C.)

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1.Unified Treatment of the Conic Sections 2.Introduction of the terms, Parabola, Ellipse, and Hyperbola 3.Hints of Analytic Geometry Mathematics in Western Culture, Morris Kline, Oxford University Press, London, 1953, p 49

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G. Alexandria and Beyond

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