Euclid's axiomatization was often thought to provide the paradigm of knowledge , by making deductive steps from necessary and self-evident truths. But as the parallel axiom, in particular, seemed less obvious than the others, many attempts were made to derive it from them. If it were derivable, then by adding its negation to the others a contradiction would be deducible from the new axiom set. In the nineteenth century Bolyai, Lobachevsky, and Riemann deduced more theorems, and proposed these systems as independent 'non-Euclidean' geometries. It has since been shown that if Euclid's geometry is consistent then so are the others, so presumably all are.
Most physicists now believe that space is non-Euclidean.
At least it is not necessarily Euclidean, as many philosophers had argued or assumed. A.J.L. See also Space-time . The Oxford Companion to Philosophy 2. The Penguin Dictionary of Psychology 5. All rights reserved.