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 Graph## Explore with Wolfram|Alpha

## Cite this as:

Weisstein, Eric W. "Pasch's Theorem."
From *MathWorld*--A Wolfram Web Resource. https://mathworld.wolfram.com/PaschsTheorem.html