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parallel postulate

Translation
parallel postulate
the axiom in Euclidean geometry that only one line can be drawn through a given point so that the line is parallel to a given line that does not contain the point. Also called parallel axiom.

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One of the five postulates, or axioms, of Euclid underpinning Euclidean geometry.

It states that through any given point not on a line there passes exactly one line parallel to that line in the same plane. Unlike Euclid's other four postulates, it never seemed entirely self-evident, as attested by efforts to prove it through the centuries. The uniqueness of Euclidean geometry, and the absolute identification of mathematics with reality, was broken in the 19th century when Nikolay Lobachevsky and János Bolyai (1802–60) independently discovered that altering the parallel postulate resulted in perfectly consistent non-Euclidean geometries.

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Universalium. 2010.

  
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