Euclid's postulate

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Related to Euclid's postulate: Euclid's fifth axiom
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Noun1.Euclid's postulate - (mathematics) any of five axioms that are generally recognized as the basis for Euclidean geometry
math, mathematics, maths - a science (or group of related sciences) dealing with the logic of quantity and shape and arrangement
Euclid's first axiom - a straight line can be drawn between any two points
Euclid's second axiom - any terminated straight line can be projected indefinitely
Euclid's third axiom - a circle with any radius can be drawn around any point
Euclid's fourth axiom - all right angles are equal
Euclid's fifth axiom, parallel axiom - only one line can be drawn through a point parallel to another line
axiom - (logic) a proposition that is not susceptible of proof or disproof; its truth is assumed to be self-evident
Based on WordNet 3.0, Farlex clipart collection. © 2003-2012 Princeton University, Farlex Inc.
References in periodicals archive ?
Apart from Euclid's Postulate, there is no guarantee that parallel lines cannot meet.
The statement in question had been the necessary result of his own commentary on Euclid's postulate. Geminus expressed it in the form of an interrogation inspired by an evident doubt raised by the work: `whether parallel lines that converge towards each other in the same way as the asymptotes of a hyperbola exist?' It is not difficult to detect behind the question posed by Geminus about the existence of asymptotic parallels the purely speculative enquiry which was born in the still-mute world of the transcendent: could another world exist, a non-Euclidean world?
Moreover, the development of non-Euclidean geometries, which overturned Euclid's postulate that parallel lines never meet, provided alternative but perfectly consistent models of reality.