Pasch's axiom

The fact that segments AC and BC are not both intersected by the line a is proved in Supplement I,1, which was written by P.

(In case the third side is parallel to our line, we count an "intersection at infinity" as external.)

A more informal version of the axiom is often seen: A more informal version of Pasch's axiom — If a line, not passing through any vertex of a triangle, meets one side of the triangle then it meets another side.

The axiom was part of Pasch's approach to introducing the concept of order into plane geometry.

There is no mention of internal and external intersections in the statement of the Veblen-Young axiom which is only concerned with the incidence property of the lines meeting.