The History of Mathematics: A Source-Based Approach

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Cover Title page Copyright Contents Acknowledgments Permissions & Acknowledgments Chapter 1. Introduction Chapter 2. Early Mathematics Introduction 2.1. Early counting 2.2. Egyptian mathematics 2.3. Mesopotamian mathematics 2.4. A historical case study 2.5. Further reading Chapter 3. Greek Mathematics: An Introduction Introduction 3.1. A dialogue from Plato’s Meno 3.2. Geometry before Plato 3.3. Plato and Aristotle 3.4. Euclid’s Elements 3.5. Further reading Chapter 4. Greek Mathematics: Proofs and Problems Introduction 4.1. The development of proof 4.2. Methods of proof 4.3. Doubling the cube and trisecting an angle 4.4. Squaring the circle 4.5. Further reading Chapter 5. Greek Mathematics: Curves Introduction 5.1. Problems with curves 5.2. Archimedes 5.3. Conics 5.4. Further reading Chapter 6. Greek Mathematics: Later Years Introduction 6.1. The Hellenistic world 6.2. Ptolemy and astronomy 6.3. Diophantus 6.4. The commentating tradition 6.5. Further reading Chapter 7. Mathematics in India and China Introduction 7.1. Indian mathematics 7.2. Chinese mathematics 7.3. Further reading Chapter 8. Mathematics in the Islamic World Introduction 8.1. The Islamic intellectual world 8.2. Islamic algebra 8.3. Islamic geometry 8.4. Further reading Chapter 9. The Mathematical Awakening of Europe Introduction 9.1. Mathematics in the medieval Christian West 9.2. The rise of the universities 9.3. Further reading Chapter 10. The Renaissance: Recovery and Innovation Introduction 10.1. Early European mathematics 10.2. Renaissance translators: Maurolico andCommandino 10.3. Cubics and quartics in 16th-century Italy 10.4. Bombelli and Viète 10.5. Further reading Chapter 11. The Renaissance of Mathematics in Britain Introduction 11.1. Mathematics in the vernacular: Robert Recorde 11.2. Mathematics for the Commonwealth:John Dee 11.3. The mathematical practitioners 11.4. Thomas Harriot 11.5. Excellent briefe rules: Napier and Briggs 11.6. Further reading Chapter 12. The Astronomical Revolution Introduction 12.1. The Copernican revolution 12.2. Kepler 12.3. The language of nature: Galileo 12.4. Further reading Chapter 13. European Mathematics in the Early 17th Century Introduction 13.1. Algebra and analysis 13.2. Fermat’s number theory 13.3. Descartes 13.4. Pappus’s locus problem 13.5. The Cartesian challenge to Euclid 13.6. Further reading Chapter 14. Concluding Remarks Chapter 15. Exercises Advice on tackling the exercises Exercises: Part A Exercises: Part B Exercises: Part C Bibliography Index Back Cover