Redefining Geometrical Exactness

Descartes’ Transformation of the Early Modern Concept of Construction

Authors:

ISBN: 978-1-4612-6521-4 (Print) 978-1-4613-0087-8 (Online)

Table of contents (29 chapters)

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  1. Front Matter

    Pages i-xix

  2. The Early Modern Tradition of Geometrical Problem Solving

    1. Front Matter

      Pages 1-1

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      Chapter

      Pages 3-22

      General introduction

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      Chapter

      Pages 23-36

      The legitimation of geometrical procedures before 1590

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      Chapter

      Pages 37-57

      1588: Pappus’ “Collection”

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      Chapter

      Pages 59-94

      The early modern tradition of geometrical problem solving; survey and examples

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      Chapter

      Pages 95-117

      Early modern methods of analysis

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      Chapter

      Pages 119-134

      Arithmetic, geometry, algebra, and analysis

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      Chapter

      Pages 135-143

      Using numbers in geometry — Regiomontanus and Stevin

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      Chapter

      Pages 145-158

      Using algebra — Viète’s analysis

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      Chapter

      Pages 159-166

      Clavius

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      Chapter

      Pages 167-181

      Viète

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      Chapter

      Pages 183-194

      Kepler

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      Chapter

      Pages 195-204

      Molther

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      Chapter

      Pages 205-210

      Fermat

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      Chapter

      Pages 211-221

      Geometrical problem solving — the state of the art c. 1635

  3. Redefining Exactness: Descartes’ Geometry

    1. Front Matter

      Pages 223-223

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      Chapter

      Pages 225-229

      Introduction to Part II

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      Chapter

      Pages 231-253

      Construction and the interpretation of exactness in Descartes’ studies of c. 1619

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      Chapter

      Pages 255-260

      Descartes’ general construction of solid problems c. 1625

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      Chapter

      Pages 261-270

      Problem solving and construction in the “Rules for the direction of the mind” (c. 1628)

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      Chapter

      Pages 271-283

      Descartes’ first studies of Pappus’ problem (early 1632)

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      Chapter

      Pages 285-291

      The Geometry, introduction and survey

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