Axiom:Pasch's Axiom (Euclidean Geometry)

Axiom
Let a triangle and a straight line lie in the same plane such that the line does not go through any of the vertices of the triangle.

Then if the line intersects one side of the triangle, it intersects another.


 * Pasch's Axiom.png

That is, such a straight line intersects two of the triangle's sides or none.

Comment
This result is used by implicitly in, but it can not be derived from the postulates.

He published this axiom in 1882, thereby showing that Euclid's postulates are incomplete.

Also see

 * Pasch's Axiom in Tarski's Geometry