# Théorème de Pasch

Pasch's theorem Not to be confused with Pasch's axiom regarding a line through a triangle.

En géométrie, Théorème de Pasch, stated in 1882 by the German mathematician Moritz Pasch,[1] is a result in plane geometry which cannot be derived from Euclid's postulates.

Contenu 1 Déclaration 2 Voir également 3 Remarques 4 Références 5 External links Statement The statement is as follows: Pasch's theorem — Given points a, b, c, and d on a line, if it is known that the points are ordered as (un, b, c) et (b, c, ré), then it is also true that (un, b, ré).[2] [Ici, par exemple, (un, b, c) means that point b lies between points a and c.] See also Ordered geometry Pasch's axiom Notes ^ Pasch 1912 ^ Coxter (1969, p. 179) states the result in 12.274 but does not refer to it specifically as Pasch's theorem. Références Coxeter, H.S.M. (1969), Introduction to geometry (2sd éd.), John Wiley and Sons, ISBN 978-0-471-18283-2, Zbl 0181.48101 Pasch, Moritz (1912) [first edition 1882], Vorlesungen uber neuere Geometrie (en allemand) (2sd éd.), Leipzig: B.G. Teubner External links Weisstein, Eric W. "Pasch's Theorem". MathWorld. This elementary geometry-related article is a stub. Vous pouvez aider Wikipédia en l'agrandissant.

Catégories: Euclidean plane geometryFoundations of geometryOrder theoryTheorems in plane geometryElementary geometry stubs

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