parallel postulate noun1 •An axiom in Euclidean geometry: given a straight line L and a point p not on L, there exists exactly one straight line parallel to L that passes through p; a variant of this axiom, such that the number of lines parallel to L that pass through p may be zero or more than one.Before we examine the particulars of the parallel postulates of Hyperbolic and Elliptical geometries, we must see their logic. — 1962 formsparallel postulates