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parallel postulate

noun

Etymology

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.

Definitions

  1. An axiom in Euclidean geometry

    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.
    • The earliest known attempt to prove the parallel postulates from the other axioms was by Ptolemy in about 150 A.D.

The neighborhood

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sense glosses and etymology drawn from English Wiktionary · source · CC-BY-SA