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.

Look at other dictionaries:

  • Parallel postulate — In geometry, the parallel postulate, also called Euclid s fifth postulate since it is the fifth postulate in Euclid s Elements , is a distinctive axiom in what is now called Euclidean geometry. It states that: If a line segment intersects two… …   Wikipedia

  • parallel postulate — noun : a postulate in geometry: if a straight line incident on two straight lines make the sum of the angles within and on the same side less than two right angles the two straight lines being produced indefinitely meet one another on whichever… …   Useful english dictionary

  • Schopenhauer's criticism of the proofs of the parallel postulate — Arthur Schopenhauer criticized mathematicians attempts to prove Euclid s Parallel Postulate because they try to prove from indirect concepts that which is directly evident from perception. Throughout his writings [ I wanted in this way to stress… …   Wikipedia

  • Parallel (geometry) — Parallelism is a term in geometry and in everyday life that refers to a property in Euclidean space of two or more lines or planes, or a combination of these. The assumed existence and properties of parallel lines are the basis of Euclid s… …   Wikipedia

  • parallel axiom — noun only one line can be drawn through a point parallel to another line • Syn: ↑Euclid s fifth axiom • Hypernyms: ↑Euclid s axiom, ↑Euclid s postulate, ↑Euclidean axiom * * * noun : parallel postul …   Useful english dictionary

  • parallel — parallelable, adj. parallelless, adj. parallelly, adv. /par euh lel , leuhl/, adj., n., v., paralleled, paralleling or (esp. Brit.) parallelled, parallelling. adj. 1. extending in the same direction, equidistant at all points, and never… …   Universalium

  • parallel axiom — Geom. See parallel postulate. * * * …   Universalium

  • AA postulate — The AA Postulate in Euclidean geometry states that two triangles are similar if they have two corresponding angles congruent.The AA Postulate works because the interior angles of a triangle are always equal to 180°. By knowing two angles, such as …   Wikipedia

  • Euclid's postulate — noun (mathematics) any of five axioms that are generally recognized as the basis for Euclidean geometry • Syn: ↑Euclid s axiom, ↑Euclidean axiom • Topics: ↑mathematics, ↑math, ↑maths • …   Useful english dictionary

  • axiom of parallels — parallel postulate …   Useful english dictionary

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