parallel axiom

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Related to Parallel postulate: Euclid's fifth axiom

parallel axiom

[¦par·ə‚lel ′ak·sē·əm]
(mathematics)
The axiom of an affine plane which states that if p and L are a point and line in the plane such that p is not on L, then there exists exactly one line that passes through p and does not intersect L.
References in periodicals archive ?
However, they felt uneasy about the parallel postulate because it was more complicated to state than the other axioms, and not quite as obviously true.
Incidentally, there were some serious attempts at proofs of the parallel postulate, but they all turned out to depend on hidden assumptions that were themselves equivalent to the parallel postulate (as is obvious if one bears hyperbolic geometry in mind).
Finally, in 1871, Klein proved that the entire theory of Projective Geometry is independent of the Parallel Postulate.

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