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Look Inside Symbols, Impossible Numbers, and Geometric Entanglements

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

$57.00 (C)

  • Date Published: November 2006
  • availability: Available
  • format: Paperback
  • isbn: 9780521027403

$ 57.00 (C)
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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.

    • Offers case study in the early reception of symbolic reasoning, which eventually changed mathematics, logic, philosophy and language studies
    • Positions British algebra of the seventeenth and early eighteenth centuries in the Scientific Revolution
    • Offers a broad, sociocultural case study of an evolving mathematical discipline, establishing connections between algebra and contemporary currents in British education, philosophy and religion
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    Reviews & endorsements

    "In her book Symbols, Impossible Numbers, and Geometric Entanglements, Helena Pycior paints a novel picture of British mathematical development in the seventeenth and eighteenth centuries. She has brought together much interesting material whose implications will interest scholars for years to come." Joan L. Richards, Isis

    "This remarkable book describes the history of the development of British algebra in the seventeenth and early eighteenth centuries (early modern algebra), focusing on attention on the constitution of algebraic language." Massimo Galuzzi, Mathematical Reviews

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    Product details

    • Date Published: November 2006
    • format: Paperback
    • isbn: 9780521027403
    • length: 344 pages
    • dimensions: 228 x 152 x 21 mm
    • weight: 0.519kg
    • contains: 3 b/w illus.
    • availability: Available
  • Table of Contents

    Acknowledgements
    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 thelogical institutes of the mathematician'.

  • Author

    Helena M. Pycior, University of Wisconsin, Milwaukee

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