aristotle and mathematics. a. hippocrates of chios (460-380 b.c.)

Aristotleand

Mathematics

Aristotleand

Mathematics

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

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

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

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

1. Orderly Arrangement of Theorems2. Indirect Method of Proof3. Author of a Geometry Text4. Calculation of Curvilinear Areas

Mathematical Thought From Ancient to Modern Times, Morris Kline, Oxford University Press, New York, 1972, p.41

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

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

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

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

• 1. Use of Explicit Axioms• 2. Method of Exhaustion

http://blog.ratestogo.com/wp-content/uploads/2009/06/athens1.jpg

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

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

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

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

• 1. Member of Plato’s 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

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

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

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

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

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

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

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

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

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

• 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

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

(262-190 B.C.)

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

(262-190 B.C.)

• 1. Unified Treatment of the Conic Sections

• 2. Introduction of the terms, Parabola, Ellipse,and Hyperbola

• 3. Hints of AnalyticGeometry

Mathematics in Western Culture, Morris Kline,Oxford University Press, London, 1953, p 49

G. Alexandria and Beyond

G. Alexandria and Beyond

http://image.linkinn.com/userfiles/Image/europe_map_1000.jpg