Symbols, Impossible Numbers, and Geometric Entanglements: British Algebra Through the Commentaries on Newton's Universal Arithmetick

Cambridge University Press, 2 nov. 2006 - 344 pages
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Symbols, Impossible Numbers, and Geometric Entanglements is the first history of the development and reception of algebra in early modern England and Scotland. Not primarily a technical history, this book analyzes the struggles of a dozen British thinkers to come to terms with early modern algebra, its symbolical style, and negative and imaginary numbers. Professor Pycior uncovers these thinkers as a "test-group" for the symbolic reasoning that would radically change not only mathematics but also logic, philosophy, and language studies. The book also shows how pedagogical and religious concerns shaped the British debate over the relative merits of algebra and geometry. The first book to position algebra firmly in the Scientific Revolution and pursue Newton the algebraist, it highlights Newton's role in completing the evolution of algebra from an esoteric subject into a major focus of British mathematics. Other thinkers covered include Oughtred, Harriot, Wallis, Hobbes, Barrow, Berkeley, and MacLaurin.

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Table des matières

Setting the Scene The Foundations of Early Modern Algebra
William Oughtred and Thomas Harriot Inciting Assisting and Instructing Others in the Analytic Art
John Collinss Campaign for a Current English Algebra Textbook The 1660s and 1670s
John Pells English Edition of Rahns Algebra and John Kerseys Algebra
The Arithmetic Formulation of Algebra in John Walliss Treatise of Algebra
English Mathematical Thinkers Take Sides on Early Modern Algebra Thomas Hobbes and Isaac Barrow against John Walks
The Mixed Mathematical Legacy of Newtons Universal Arithmetick
George Berkeley at the Intersection of Algebra and Philosophy
The Scottish Response to Newtonian Algebra
Algebra Considered As the Logical Institutes of the Mathematician Nicholas Saundersons Elements of Algebra
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