1. Aristotle and Mathematics

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

3. 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

4. B.Eudoxus of Cnidus (408-355 B.C.)

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

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

7. 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

8. 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

9. D.Euclid (c. 325-265 B.C.)

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

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

12. 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

13. F. Apollonius (262-190 B.C.)

14. 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

15. G. Alexandria and Beyond http://image.linkinn.com/userfiles/Image/europe_map_1000.jpg