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Mathematical thought from ancient to modern times. volume 1 /
This comprehensive history traces the development of mathematical ideas and the careers of the mathematicians responsible for them. Volume 1 looks at the discipline's origins in Babylon and Egypt, the creation of geometry and trigonometry by the Greeks, and the role of mathematics in the mediev...
| Clasificación: | Libro Electrónico |
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| Autor principal: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
New York ; Oxford :
Oxford University Press,
1990, ©1972.
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| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- Cover Page; Title Page; Copyright Page; Dedication; Preface to the Three-Volume: Paperback Edition of Mathematical Thought; Preface; Contents; Publisher's Note; 1. Mathematics in Mesopotamia; 1. Where Did Mathematics Begin?; 2. Political History in Mesopotamia; 3. The Number Symbols; 4. Arithmetic Operations; 5. Babylonian Algebra; 6. Babylonian Geometry; 7. The Uses of Mathematics in Babylonia; 8. Evaluation of Babylonian Mathematics; 2. Egyptian Mathematics; 1. Background; 2. The Arithmetic; 3. Algebra and Geometry; 4. Egyptian Uses of Mathematics; 5. Summary.
- 3. The Creation of Classical Greek Mathematics1. Background; 2. The General Sources; 3. The Major Schools of the Classical Period; 4. The Ionian School; 5. The Pythagoreans; 6. The Eleatic School; 7. The Sophist School; 8. The Platonic School; 9. The School of Eudoxus; 10. Aristotle and His School; 4. Euclid and Apollonius; 1. Introduction; 2. The Background of Euclid's Elements; 3. The Definitions and Axioms of the Elements; 4. Books I to IV of the Elements; 5. Book V: The Theory of Proportion; 6. Book VI: Similar Figures; 7. Books VII, VIII, and IX: TheTheory of Numbers.
- 8. Book X: The Classification of Incommensurables9. Books XI, XII, and XIII: Solid Geometry and the Method of Exhaustion; 10. The Merits and Defects of the Elements; 11. Other Mathematical Works by Euclid; 12. The Mathematical Work of Apollonius; 5. The Alexandrian Greek Period: Geometry and Trigonometry; 1. The Founding of Alexandria; 2. The Character of Alexandrian Greek Mathematics; 3. Areas and Volumes in the Work of Archimedes; 4. Areas and Volumes in the Work of Heron; 5. Some Exceptional Curves; 6. The Creation of Trigonometry; 7. Late Alexandrian Activity in Geometry.
- 6. The Alexandrian Period: The Reemergence of Arithmetic and Algebra1. The Symbols and Operations of Greek Arithmetic; 2. Arithmetic and Algebra as an Independent Development; 7. The Greek Rationalization of Nature; 1. The Inspiration for Greek Mathematics; 2. The Beginnings of a Rational View of Nature; 3. The Development of the Belief in Mathematical Design; 4. Greek Mathematical Astronomy; 5. Geography; 6. Mechanics; 7. Optics; 8. Astrology; 8. The Demise of the Greek World; 1. A Review of the Greek Achievements; 2. The Limitations of Greek Mathematics.
- 3. The Problems Bequeathed by the Greeks4. The Demise of the Greek Civilization; 9. The Mathematics of the Hindus and Arabs; 1. Early Hindu Mathematics; 2. Hindu Arithmetic and Algebra of the Period A.D. 200-1200; 3. Hindu Geometry and Trigonometry of the Period A.D. 200-1200; 4. The Arabs; 5. Arabic Arithmetic and Algebra; 6. Arabic Geometry and Trigonometry; 7. Mathematics circa 1300; 10. The Medieval Period in Europe; 1. The Beginnings of a European Civilization; 2. The Materials Available for Learning; 3. The Role of Mathematics in Early Medieval Europe; 4. The Stagnation in Mathematics.