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