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Book contents
- Frontmatter
- Contents
- Acknowledgments
- Introduction
- 1 Setting the Scene
- 2 William Oughtred and Thomas Harriot
- 3 John Collins's Campaign for a Current English Algebra Textbook
- 4 John Pell's English Edition of Rahn's Algebra and John Kersey's Algebra
- 5 The Arithmetic Formulation of Algebra in John Wallis's Treatise of Algebra
- 6 English Mathematical Thinkers Take Sides on Early Modern Algebra
- 7 The Mixed Mathematical Legacy of Newton's Universal Arithmetick
- 8 George Berkeley at the Intersection of Algebra and Philosophy
- 9 The Scottish Response to Newtonian Algebra
- 10 Algebra “Considered As the Logical Institutes of the Mathematician”
- Epilogue
- Index
1 - Setting the Scene
The Foundations of Early Modern Algebra
Published online by Cambridge University Press: 05 December 2011
- Frontmatter
- Contents
- Acknowledgments
- Introduction
- 1 Setting the Scene
- 2 William Oughtred and Thomas Harriot
- 3 John Collins's Campaign for a Current English Algebra Textbook
- 4 John Pell's English Edition of Rahn's Algebra and John Kersey's Algebra
- 5 The Arithmetic Formulation of Algebra in John Wallis's Treatise of Algebra
- 6 English Mathematical Thinkers Take Sides on Early Modern Algebra
- 7 The Mixed Mathematical Legacy of Newton's Universal Arithmetick
- 8 George Berkeley at the Intersection of Algebra and Philosophy
- 9 The Scottish Response to Newtonian Algebra
- 10 Algebra “Considered As the Logical Institutes of the Mathematician”
- Epilogue
- Index
Summary
In this book, learned reader, you have the rules of algebra (in Italian, the rules of the coss). It is so replete with new discoveries and demonstrations by the author – more than seventy of them – that its forerunners [are] of little account or, in the vernacular, are washed out.
Thus the very advertisement to Girolamo Cardano's Great Art (Ars magna) suggested the dawning of a new epoch in the algebra of the Western world. Although less original than implied here, The Great Art – published in 1545, just two years after Copernicus's De revolutionibus and Vesalius's De fabrica – was an exciting scientific classic. Exciting in the mathematical way, the work announced the solution of two hitherto unsolved problems, finding the roots of cubic and quartic (or biquadratic) equations. As many other classics, it helped to redefine its field. In particular, it fostered an expanding universe of algebraic objects through its consistent acknowledgment of negative roots as well as its brush with imaginary roots.
Still, The Great Art was not solely responsible for the major reconstruction that Western algebra underwent in the sixteenth and early seventeenth centuries. Algebra's reconstruction involved new results, objects, language, methodological justification, and a changing relationship with geometry. It was as much due to Francois Viète's Analytic Art as to Cardano's Great Art.
- Type
- Chapter
- Information
- Symbols, Impossible Numbers, and Geometric EntanglementsBritish Algebra through the Commentaries on Newton's Universal Arithmetick, pp. 10 - 39Publisher: Cambridge University PressPrint publication year: 1997