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

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References

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

Cite this as:

Weisstein, Eric W. "Proclus' Axiom." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/ProclusAxiom.html

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