Pasch's Theorem

A theorem stated in 1882 which cannot be derived from Euclid's postulates. Given points a, b, c, and d on a line, if it is known that the points are ordered as (a,b,c) and (b,c,d), then it is also true that (a,b,d).

See also

Euclid's Postulates, Line, Pasch's Axiom, Pasch Configuration, Pasch Graph

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Cite this as:

Weisstein, Eric W. "Pasch's Theorem." From MathWorld--A Wolfram Web Resource.

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