n. the axiom of Euclidean geometry stating that if two straight lines are cut by a third, the two will meet on the side of the third on which the sum of the interior angles is less than two right angles; equivalently, Playfair's axiom states that through a given point only one line can be drawn parallel to a given line. This was regarded as self-evident until the 19th century, when non-Euclidean geometries were devised in which all the remaining axioms of Euclidean geometry were retained, but this was false. Since these other geometries are consistent, the parallel postulate must be independent of the remaining Euclidean axioms.