Described in Proposition 29, it was shown to be independent of four earlier statements of the same kind.
Arthur Schopenhauer criticized attempted proofs of this statement from concepts rather than using perception, and G.S. Klügel demonstrated how 28 attempted proofs of it were wrong. It can be equated to Proclus' axiom, and a stronger version of it is Playfair's axiom. Described in Proposition 29, it was shown to be independent of four earlier statements of the same kind. Bolyai, Lobachevsky, and Riemann have all developed geometries in which it doesn't hold. For 10 points, name this fifth postulate in Euclid's Elements, which deals with lines that never intersect.
Arthur Schopenhauer criticized attempted proofs of this statement from concepts rather than using perception, and G.S. Klügel demonstrated how 28 attempted proofs of it were wrong.
{parallel} postulate [accept {Euclid's fifth postulate} before read]