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Aristotle and Mathematics

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A. Hippocrates of Chios (460-380 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 (408-355 B.C.)

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1.Use of Explicit Axioms 2.Method of Exhaustion http://blog.ratestogo.com/wp-content/uploads/2009/06/athens1.jpg

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C. Aristotle (384-322 B.C.)

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1.Member of Platos Academy 2.Founder of the Lyceum http://www.anampa.gr/anaweb/getimage?action=imgrep&filePath=/apps1/Image/200907/DOC.20090709.7775228.ars1.jpg http://users.ntua.gr/chgantes/en/txtimg/steel_roof_Aristotle_Lyceum.jpg

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C. Aristotle (384-322 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. 325-265 B.C.)

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

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E. Archimedes (287-212 B.C.)

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1.Calculation of Areas and Volumes 2.Excellent Estimate of Pi 3.Law of Levers 4.Hydrostatics http://www.math.nyu.edu/~crorres/Archimedes/Tomb/Cicero.html

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F. Apollonius (262-190 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 http://image.linkinn.com/userfiles/Image/europe_map_1000.jpg

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