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The Possibility of Non-Euclidean Geometry

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Abstract

By the latter half of the 18th century the problem of deducing Postulate 5 from Neutral geometry had become, in mathematical circles, notorious. The Encyclopedist Jean le Rond d’Alembert called it (1759) “le scandale des éléments de géométrie.”

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Notes

  1. clamor. Letter to F. W. Bessel, January 27, 1829.

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  2. polernie. Letter to H. K. Schumacher.

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  3. lifetime. Letter to Farkas Bolyai, March 6, 1832.

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  4. it should not perish with me. Letter to H. K. Schumacher, May 17, 1831 .

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  5. such a remarkable manner. Letter to Farkas Bolyai, March 6, 1832.

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  6. Pattern for a Formal Axiomatic System. From Eves, A Survey of Geometry (Allyn and Bacon, 1972), p. 338.

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  7. The Scorpling Flugs. After Eves, op. cit., p. 340, problem 3.

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© 2001 Birkhäuser Boston

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Trudeau, R.J. (2001). The Possibility of Non-Euclidean Geometry. In: The Non-Euclidean Revolution. Birkhäuser Boston. https://doi.org/10.1007/978-1-4612-2102-9_5

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  • DOI: https://doi.org/10.1007/978-1-4612-2102-9_5

  • Publisher Name: Birkhäuser Boston

  • Print ISBN: 978-0-8176-4237-2

  • Online ISBN: 978-1-4612-2102-9

  • eBook Packages: Springer Book Archive

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