In geometry, the parallel postulate, also called Euclid's fifth postulate because it is the fifth postulate in Euclid's Elements, is a distinctive axiom...
25 KB (3,227 words) - 15:48, 6 August 2024
Arthur Schopenhauer (redirect from Arthur Schopenhauer's criticism of the proofs of the parallel postulate)
evident in his criticism of contemporaneous attempts to prove the parallel postulate in Euclidean geometry. Writing shortly before the discovery of hyperbolic...
152 KB (19,827 words) - 06:52, 20 August 2024
Euclidean geometry (redirect from Euclid's second postulate)
seemed so intuitively obvious (with the possible exception of the parallel postulate) that theorems proved from them were deemed absolutely true, and thus...
59 KB (7,080 words) - 06:43, 5 August 2024
Sum of angles of a triangle (redirect from Triangle postulate)
triangle postulate states that the sum of the angles of a triangle is two right angles. This postulate is equivalent to the parallel postulate. In the...
7 KB (815 words) - 04:12, 12 August 2024
direction (not necessarily the same length). Parallel lines are the subject of Euclid's parallel postulate. Parallelism is primarily a property of affine...
23 KB (2,793 words) - 22:21, 22 August 2024
Playfair's axiom (redirect from Playfair's Postulate)
instead of the fifth postulate of Euclid (the parallel postulate): In a plane, given a line and a point not on it, at most one line parallel to the given line...
12 KB (1,594 words) - 23:50, 8 November 2023
affine geometry, non-Euclidean geometry arises by either replacing the parallel postulate with an alternative, or relaxing the metric requirement. In the former...
44 KB (6,018 words) - 09:27, 4 August 2024
seemed so intuitively obvious (with the possible exception of the parallel postulate) that any theorem proved from them was deemed true in an absolute...
76 KB (10,902 words) - 02:44, 15 June 2024
consequence of the Euclidean parallel postulate and neither condition can be proven without appealing to the Euclidean parallel postulate or one of its equivalent...
15 KB (1,985 words) - 00:13, 14 August 2024