The Fifth Postulate

"One of Euclid's postulates – his postulate 5 - had the fortune to be an epoch-making statement – perhaps the most famous single utterance in the history of science" (Wolfe, 1945, p.17). The fifth postulate exclaims that "if a straight line falling on two straight lines make the interior angles on the same side less than two right angles, the two straight lines, if produced indefinitely, meet on that side on which are angles less than the two right angles" (Wolf, 1945, p.4), (see fig 2). In other words, the fifth postulate exclaims that one and only one line can be drawn parallel to a given line through a given external point. With the many attempts mathematicians made to prove this thesis over the years, it seems ironic that what stole the lights with a flawless well-rounded proof were actually its antitheses. Although this new geometry attracted little attention for over thirty-five years, the honored mathematicians, Gauss and Riemann in Germany, Bolyai in Hungary and Lobachevski in Russia were busy trying to take a strategic place in the history as the founders of non-Euclidean geometry.

Reference: Wolf, H.E. (1945). Introduction to non-Euclidean geometry
Euclid's fifth, n.d, n.t, google image, retrieved on 4/11/2009
http://www-math.cudenver.edu/~wcherowi/courses/m3210/hghw23p1.gif