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On The Pseudo-Euclidean Geometry Due to G. Hessenberg

Published online by Cambridge University Press:  20 November 2018

Paul Szász
Paul Szász*
Affiliation:
Loránd Eötvös University, Budapest, Hungary
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G. Hessenberg (2) showed that euclidean plane geometry can be realized on the surface of the sphere without assuming the parallel axiom. This geometry will be called the pseudo-euclidean geometry due to G. Hessenberg. In the present paper we give a slightly different treatment, which is perhaps simpler than that of Hessenberg and which has a greater transparency.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 19 , 1967 , pp. 1218 - 1232
Copyright
Copyright © Canadian Mathematical Society 1967

References

1. Forder, H. G., The foundations of euclidean geometry (Dover Publications, New York, 1958).Google Scholar
2. Hessenberg, G., Bergründung der elliptischen Geometrie, Math. Ann., 61 (1905), 173–184.Google Scholar
3. Hilbert, D., Grundlagen der Geomtrie, 9. Aufl. (Stuttgart, 1962).Google Scholar
4. Kerékjärtó, B., Les fondements de la géométrie, Vol. 1 (Budapest, 1955).Google Scholar
5. Liebmann, H., Begründung der sphärischen Trigonometrie, … , Ber. Verh. Sachs. Akad. Wiss. Leipzig, Math.—Nat. Kl., 60 (1908), 289–305.Google Scholar
6. Mansion, P., Essai d'exposition élémentaire des principes fondamentaux de la géométrie non euclidienne de Riemann, Mathesis, 2e série, t. 5 (1895), Supplement, février 1895, pp. 8–21.Google Scholar