Etymology

parallel postulate

Today it means: 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. Full definition →

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The story

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

Etymology from Wiktionary, CC BY-SA 4.0.