What victory heralded the great rocket for which young lobachevski, the widow's son, was cast into prison?
lobachevski has proved not, by creating non-Euclidean geometry.
There is a sort of opposition between Riemann's geometry and that of lobachevski.
Beltrami has shown that the geometry of these surfaces is none other than that of lobachevski.
The two-dimensional geometries of Riemann and lobachevski are thus correlated to the Euclidean geometry.
Thus, however far the consequences of lobachevski's hypotheses are pushed, they will never lead to a contradiction.
If lobachevski's geometry is true, the parallax of a very distant star will be finite; if Riemann's is true, it will be negative.
If this were so, experience would be capable of deciding between the hypothesis of Euclid and that of lobachevski.
What is important is the conclusion: experiment can not decide between Euclid and lobachevski.