Through any point in the plane, there is at most one straight line parallel to a given straight line. This axiom is equivalent to the parallel postulate.
Playfair's Axiom
See also
Parallel PostulateExplore with Wolfram|Alpha
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.Henderson, D. W. Experiencing Geometry: On Plane and Sphere. Englewood Cliffs, NJ: Prentice-Hall, 1995.Playfair, J. Elements of Geometry: Containing the First Six Books of Euclid, with a Supplement on the Circle and the Geometry of Solids to which are added Elements of Plane and Spherical Trigonometry. New York: W. E. Dean, 1861.Referenced on Wolfram|Alpha
Playfair's AxiomCite this as:
Weisstein, Eric W. "Playfair's Axiom." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/PlayfairsAxiom.html