A theorem stated in 1882 which cannot be derived from Euclid's postulates. Given points , , , and on a line, if it is known that the points are ordered as and , then it is also true that .
Pasch's Theorem
See also
Euclid's Postulates, Line, Pasch's Axiom, Pasch Configuration, Pasch GraphExplore with Wolfram|Alpha
Cite this as:
Weisstein, Eric W. "Pasch's Theorem." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/PaschsTheorem.html