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.
If this were so, experience would be capable of deciding between the hypothesis of Euclid and that of lobachevski.
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.
What is important is the conclusion: experiment can not decide between Euclid and lobachevski.
What victory heralded the great rocket for which young lobachevski, the widow's son, was cast into prison?