Proclus' Axiom

If a line intersects one of two parallel lines, both of which are coplanar with the original line, then it must intersect the other also.

This axiom is equivalent to the parallel postulate.

See also

Coplanar, Intersection, Line-Line Intersection, Parallel Lines, Parallel Postulate

Explore with Wolfram|Alpha


Dunham, W. "Hippocrates' Quadrature of the Lune." Ch. 1 in Journey through Genius: The Great Theorems of Mathematics. New York: Wiley, p. 54, 1990.

Referenced on Wolfram|Alpha

Proclus' Axiom

Cite this as:

Weisstein, Eric W. "Proclus' Axiom." From MathWorld--A Wolfram Web Resource.

Subject classifications