This mathematical statement has been shown to be equivalent to Playfair's axiom, Proclus'.
This mathematical statement has been shown to be equivalent to Playfair's axiom, Proclus'. Axiom, and the Pythagorean theorem. Rewordings of the statement give rise to elliptic or hyperbolic geometries. If the axiom is omitted from the others with which it usually associated, the non-Euclideam geometry can be developed. Name this postulate of Euclid that assumes that given a point and a line not containing that point that there exists only one line passing through the point that does not intersect the given line.
This mathematical statement has been shown to be equivalent to Playfair's axiom, Proclus'.
{Parallel postulate} (or Euclid’s {fifth postulate})