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Historical Examples of lobachevski
Lobachevski has proved not, by creating non-Euclidean geometry.
There is a sort of opposition between Riemann's geometry and that of Lobachevski.
Thus, however far the consequences of Lobachevski's hypotheses are pushed, they will never lead to a contradiction.
The two-dimensional geometries of Riemann and Lobachevski are thus correlated to the Euclidean geometry.
Beltrami has shown that the geometry of these surfaces is none other than that of Lobachevski.