- 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 <i>Liber Abbaci</i>
- Chapter 8 Refuting Origins
- Part 2 Algebra
- Chapter 9 Sans Symbols
- Chapter 10 Diophantus’s <i>Arithmetica</i>
- 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 <i>x<sup>n</sup></i>
- Appendix C Experiment
- Appendix D Visualizing Complex Numbers
- Appendix E Quaternions
- Acknowledgments
- Index

# Vowels and Consonants

# Vowels and Consonants

- Chapter:
- (p.141) Chapter 15 Vowels and Consonants
- Source:
- Enlightening Symbols
- Author(s):
### Joseph Mazur

- Publisher:
- Princeton University Press

This chapter focuses on the evolution of the vowel–consonant notation. In particular, it discusses François Viète's contribution to algebra through his use of vowels to represent unknowns and consonants to represent known quantities. Viète, a French mathematician, expressed his famous computation for π in proposition II of his *Isagoge*. Even Christoff Rudolff and Nicolas Chuquet had no proper notation for expressing such an infinite sum of nested square roots. Viète was showing us an intimate link between Greek geometry and algebra, a link from the mathematics of lines, figures, and solids to the underlying channels of symbolic algebra. The chapter also considers Viète's work on what are now called “homogeneous equations” as well as the significance of his lettering system to symbolic algebra.

*Keywords:*
vowel-–consonant notation, François Viète, algebra, notation, nested square roots, geometry, mathematics, symbolic algebra, homogeneous equations, known quantities

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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 <i>Liber Abbaci</i>
- Chapter 8 Refuting Origins
- Part 2 Algebra
- Chapter 9 Sans Symbols
- Chapter 10 Diophantus’s <i>Arithmetica</i>
- 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 <i>x<sup>n</sup></i>
- Appendix C Experiment
- Appendix D Visualizing Complex Numbers
- Appendix E Quaternions
- Acknowledgments
- Index