Worlds Out of Nothing

A Course in the History of Geometry in the 19th Century

Authors:

ISBN: 978-0-85729-059-5 (Print) 978-0-85729-060-1 (Online)

Table of contents (31 chapters)

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  1. Front Matter

    Pages I-XXV

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    Book Chapter

    Pages 1-10

    Mathematics in the French Revolution

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    Book Chapter

    Pages 11-24

    Poncelet (and Pole and Polar)

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    Pages 25-41

    Theorems in Projective Geometry

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    Pages 43-52

    Poncelet’s Traité

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    Pages 53-61

    Duality and the Duality Controversy

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    Pages 63-78

    Poncelet, Chasles, and the Early Years of Projective Geometry

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    Pages 79-89

    Euclidean Geometry, the Parallel Postulate, and the Work of Lambert and Legendre

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    Pages 91-100

    Gauss (Schweikart and Taurinus) and Gauss’s Differential Geometry

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    Pages 101-114

    János Bolyai

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    Pages 115-127

    Lobachevskii

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    Pages 129-135

    Publication and Non-Reception up to 1855

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    Book Chapter

    Pages 137-148

    On Writing the History of Geometry – 1

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    Book Chapter

    Pages 149-159

    Across the Rhine – Möbius’s Algebraic Version of Projective Geometry

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    Pages 161-171

    Plücker, Hesse, Higher Plane Curves, and the Resolution of the Duality Paradox

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    Book Chapter

    Pages 173-178

    The Plücker Formulae

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    Book Chapter

    Pages 179-190

    The Mathematical Theory of Plane Curves

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    Pages 191-194

    Complex Curves

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    Pages 195-209

    Riemann: Geometry and Physics

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    Book Chapter

    Pages 211-225

    Differential Geometry of Surfaces

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    Book Chapter

    Pages 227-240

    Beltrami, Klein, and the Acceptance of Non-Euclidean Geometry

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