Phillip E. Parker Wichita State University In the beginning
there was geometry, and it was codified by Euclid about 300 BC.
Some 1500 years later, the contemporary thought was that there
could be only this one, true geometry. This culminated in Kant's
argument in his Critique of Pure Reason in 1781 that Euclidean
geometry was an a priori synthetic truth. Others appealed to
experience or relied on innate truths, but almost all
philosophers and mathematicians were agreed. Unfortunately for
their certitude, however, Lambert had already proved the
existence of a noneuclidean geometry in 1766, but this was not
generally known until somewhat later  and was not recognized
until much later. In 1799, Gauss was already doubting the
privileged rôle of Euclidean geometry, and by 1817 his doubt had
become assured . Meanwhile, Schweikart had found a noneuclidean
geometry by 1816 , but did not take the final step of observing
that it could not be determined if the universe were Euclidean
or not. This remained for Bolyai , b