- Title Pages
- Dedication
- Introduction
- Definitions
- Note on the Illustrations
- Part 1 Numerals: Significant Manuscripts and Initiators
- Chapter 1 Curious Beginnings
- Chapter 2 Certain Ancient Number Systems
- Chapter 3 Silk and Royal Roads
- Chapter 4 The Indian Gift
- Chapter 5 Arrival in Europe
- Chapter 6 The Arab Gift
- Chapter 7 Liber Abbaci
- Chapter 8 Refuting Origins
- Part 2 Algebra
- Chapter 9 Sans Symbols
- Chapter 10 Diophantus’s Arithmetica
- Chapter 11 The Great Art
- Chapter 12 Symbol Infancy
- Chapter 13 The Timid Symbol
- Chapter 14 Hierarchies of Dignity
- Chapter 15 Vowels and Consonants
- Chapter 16 The Explosion
- Chapter 17 A Catalogue of Symbols
- Chapter 18 The Symbol Master
- Chapter 19 The Last of the Magicians
- Part 3 The Power of Symbols
- Chapter 20 Rendezvous in the Mind
- Chapter 21 The Good Symbol
- Chapter 22 Invisible Gorillas
- Chapter 23 Mental Pictures
- Chapter 24 Conclusion
- Appendix A Leibniz’s Notation
- Appendix B Newton’s Fluxion of xn
- Appendix C Experiment
- Appendix D Visualizing Complex Numbers
- Appendix E Quaternions
- Acknowledgments
- Index
Diophantus’s Arithmetica
Diophantus’s Arithmetica
- Chapter:
- (p.93) Chapter 10 Diophantus’s Arithmetica
- Source:
- Enlightening Symbols
- Author(s):
Joseph Mazur
- Publisher:
- Princeton University Press
This chapter discusses Diophantus's Arithmetica and its contribution to symbolic modern mathematics. Some historians in the past have suggested that algebra began with Diophantus, whose Arithmetica is characterized by the crudeness of its notation. Only six of the thirteen books survive as copies of the original Arithmetica in Greek. The chapter considers the debate among scholars over the origins of a symbol used by Diophantus in Arithmetica, which also appears in Heron of Alexandria's Metrica, written in the first century AD. It suggests that Diophantus's notation does not solidly distinguish operational symbols, such as powers or summation, from numbers or indeterminate objects.
Keywords: symbols, Diophantus, Arithmetica, mathematics, algebra, notation, Heron of Alexandria, Metrica, powers
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- Title Pages
- Dedication
- Introduction
- Definitions
- Note on the Illustrations
- Part 1 Numerals: Significant Manuscripts and Initiators
- Chapter 1 Curious Beginnings
- Chapter 2 Certain Ancient Number Systems
- Chapter 3 Silk and Royal Roads
- Chapter 4 The Indian Gift
- Chapter 5 Arrival in Europe
- Chapter 6 The Arab Gift
- Chapter 7 Liber Abbaci
- Chapter 8 Refuting Origins
- Part 2 Algebra
- Chapter 9 Sans Symbols
- Chapter 10 Diophantus’s Arithmetica
- Chapter 11 The Great Art
- Chapter 12 Symbol Infancy
- Chapter 13 The Timid Symbol
- Chapter 14 Hierarchies of Dignity
- Chapter 15 Vowels and Consonants
- Chapter 16 The Explosion
- Chapter 17 A Catalogue of Symbols
- Chapter 18 The Symbol Master
- Chapter 19 The Last of the Magicians
- Part 3 The Power of Symbols
- Chapter 20 Rendezvous in the Mind
- Chapter 21 The Good Symbol
- Chapter 22 Invisible Gorillas
- Chapter 23 Mental Pictures
- Chapter 24 Conclusion
- Appendix A Leibniz’s Notation
- Appendix B Newton’s Fluxion of xn
- Appendix C Experiment
- Appendix D Visualizing Complex Numbers
- Appendix E Quaternions
- Acknowledgments
- Index