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
2 - William Oughtred and Thomas Harriot
“Inciting, Assisting, and Instructing Others” in the Analytic Art
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
Viète's symbolical style so captured the imaginations of the Englishmen William Oughtred and Thomas Harriot that at least the former seems to have taken as the mission of his advanced years the “inciting, assisting, and instructing others” in the analytic art. Both produced textbooks on the subject, which brought early modern algebra, under the guise of the analytic art, to England. Published in 1631, these symbol-laden books struck a responsive chord in an English scientific community that was beginning to favor, among other things, plain prose. By the third quarter of the century, then, there was a growing school of English analytic mathematicians; there were also the beginnings of a related drive toward the acceptance of mathematics, including algebra, as a scholarly pursuit.
Oughtred, Harriot, and their disciples shared first and foremost a deep and irrevocable commitment to symbolical reasoning. As the two English algebraic pioneers fostered Viète's symbolical style, they also perpetuated his hesitancy about the expanding algebraic universe. They and most of their immediate successors reasoned symbolically, wrote algebraic equations for geometric problems, but largely ignored negative and imaginary roots or – in the most daring of cases, including Harriot's speculations in unpublished manuscripts – struggled to make some sense of them. In short, the algebra that was imported into England through Oughtred's and Harriot's textbooks was Viète's, not Cardano's. In England, a deep appreciation of the symbolical style came first; openness to the expanding universe of algebra followed slowly.
- Type
- Chapter
- Information
- Symbols, Impossible Numbers, and Geometric EntanglementsBritish Algebra through the Commentaries on Newton's Universal Arithmetick, pp. 40 - 69Publisher: Cambridge University PressPrint publication year: 1997