Worlds Out of Nothing

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

Authors:

ISBN: 978-1-84628-632-2 (Print) 978-1-84628-633-9 (Online)

Table of contents (31 chapters)

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  1. Front Matter

    Pages i-xxiii

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    Book Chapter

    Pages 1-10

    Mathematics in the French Revolution

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    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 79-88

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

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    Pages 89-98

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

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    Pages 99-111

    János Bolyai

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    Pages 113-122

    Lobachevskii

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    Pages 123-129

    Publication and Non-Reception up to 1855

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    Pages 131-142

    On Writing the History of Geometry — 1

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    Pages 143-153

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

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    Pages 155-164

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

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    Book Chapter

    Pages 165-170

    The Plücker Formulae

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    Pages 171-182

    The Mathematical Theory of Plane Curves

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    Pages 183-186

    Complex Curves

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    Pages 187-201

    Riemann: Geometry and Physics

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    Book Chapter

    Pages 203-217

    Differential Geometry of Surfaces

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    Book Chapter

    Pages 219-232

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

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