parallel postulate

Meaning

Noun

• An axiom of Euclidean geometry equivalent to the statement that, given a straight line L and a point P not on the line, 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.

Related

Similar words

• Euclid's fifth postulate, triangle postulate

Origin

• From the reference to parallel lines in the definition as formulated below, following Scottish mathematician John Playfair; this wording leads to a convenient basic categorisation of Euclidean and non-Euclidean geometries. The original formulation in Euclid's Elements makes no mention of parallels.