Philosophy Lexicon of Arguments

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A. d'Abro Die Kontroversen über das Wesen der Mathematik 1939 in Kursbuch 8 Mathematik 1967

Riemann/d'Abro: Riemann's great contribution to the development of non-Euclidean geometry was precisely the replacement of the restricted axiomatic method of the decomposition of postulates (as Bolyai and Lobachevski practiced it) by the more effective methods of analysis. Thus, Riemann has generalized the different types of non-Euclidean geometry.
By rejecting it, it was also recognized that the axioms of Euclid could at least not be a priori. The mathematicians were forced to reject the Kantian assumption for all axioms, including the implied assumptions.
d’Abro, A.

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Ed. Martin Schulz, access date 2017-05-27