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The Possibility of Non-Euclidean Geometry

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.”

Keywords

Euclidean Geometry Axiomatic System Hyperbolic Geometry Logical Possibility Common Notion 
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Notes

  1. 4.
    clamor. Letter to F. W. Bessel, January 27, 1829.Google Scholar
  2. 5.
    polemic. Letter to H. K. Schumacher.Google Scholar
  3. 6.
    lifetime. Letter to Farkas Bolyai, March 6, 1832.Google Scholar
  4. 7.
    it should not perish with me. Letter to H. K. Schumacher, May 17, 1831.Google Scholar
  5. 8.
    such a remarkable manner. Letter to Farkas Bolyai, March 6, 1832.Google Scholar
  6. 10.
    Pattern for a Formal Axiomatic System. From Eves, A Survey of Geometry (Allyn and Bacon, 1972), p. 338.Google Scholar
  7. 11.
    The Scorpling Flugs. After Eves, op. cit., p. 340, problem 3.Google Scholar

Copyright information

© Birkhäuser Boston 2008

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