Aristotle and Mathematics
description
Transcript of Aristotle and Mathematics
![Page 1: Aristotle and Mathematics](https://reader036.fdocuments.us/reader036/viewer/2022062520/568165e8550346895dd9079a/html5/thumbnails/1.jpg)
Aristotleand
Mathematics
![Page 2: Aristotle and Mathematics](https://reader036.fdocuments.us/reader036/viewer/2022062520/568165e8550346895dd9079a/html5/thumbnails/2.jpg)
A. Hippocrates of Chios(460-380 B.C.)
![Page 3: Aristotle and Mathematics](https://reader036.fdocuments.us/reader036/viewer/2022062520/568165e8550346895dd9079a/html5/thumbnails/3.jpg)
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
![Page 4: Aristotle and Mathematics](https://reader036.fdocuments.us/reader036/viewer/2022062520/568165e8550346895dd9079a/html5/thumbnails/4.jpg)
B.Eudoxus of Cnidus(408-355 B.C.)
![Page 5: Aristotle and Mathematics](https://reader036.fdocuments.us/reader036/viewer/2022062520/568165e8550346895dd9079a/html5/thumbnails/5.jpg)
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
![Page 6: Aristotle and Mathematics](https://reader036.fdocuments.us/reader036/viewer/2022062520/568165e8550346895dd9079a/html5/thumbnails/6.jpg)
C. Aristotle(384-322 B.C.)
![Page 7: Aristotle and Mathematics](https://reader036.fdocuments.us/reader036/viewer/2022062520/568165e8550346895dd9079a/html5/thumbnails/7.jpg)
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
![Page 8: Aristotle and Mathematics](https://reader036.fdocuments.us/reader036/viewer/2022062520/568165e8550346895dd9079a/html5/thumbnails/8.jpg)
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
![Page 9: Aristotle and Mathematics](https://reader036.fdocuments.us/reader036/viewer/2022062520/568165e8550346895dd9079a/html5/thumbnails/9.jpg)
D. Euclid (c. 325-265 B.C.)
![Page 10: Aristotle and Mathematics](https://reader036.fdocuments.us/reader036/viewer/2022062520/568165e8550346895dd9079a/html5/thumbnails/10.jpg)
D. Euclid (c. 325-265 B.C.)
• 1. Axioms• 2. Definitions• 3. Deductive Approach• 4. Conic Sections
![Page 11: Aristotle and Mathematics](https://reader036.fdocuments.us/reader036/viewer/2022062520/568165e8550346895dd9079a/html5/thumbnails/11.jpg)
E. Archimedes(287-212 B.C.)
![Page 12: Aristotle and Mathematics](https://reader036.fdocuments.us/reader036/viewer/2022062520/568165e8550346895dd9079a/html5/thumbnails/12.jpg)
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
![Page 13: Aristotle and Mathematics](https://reader036.fdocuments.us/reader036/viewer/2022062520/568165e8550346895dd9079a/html5/thumbnails/13.jpg)
F. Apollonius(262-190 B.C.)
![Page 14: Aristotle and Mathematics](https://reader036.fdocuments.us/reader036/viewer/2022062520/568165e8550346895dd9079a/html5/thumbnails/14.jpg)
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
![Page 15: Aristotle and Mathematics](https://reader036.fdocuments.us/reader036/viewer/2022062520/568165e8550346895dd9079a/html5/thumbnails/15.jpg)
G. Alexandria and Beyond
http://image.linkinn.com/userfiles/Image/europe_map_1000.jpg