parallel axiom
- noun
- /ˈpærəˌlɛl ˈæksaɪəm/
- Specialized
:
axioma paralelo
- The parallel axiom states that through a given point not on a line, there is exactly one line that does not intersect the original line.
Examples
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The parallel axiom is fundamental in Euclidean geometry and distinguishes it from non-Euclidean systems.
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Many attempts were made to prove the parallel axiom from other axioms, but all failed.
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Lobachevsky developed a geometry that does not require the parallel axiom to hold.
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The parallel axiom is fundamental in Euclidean geometry.
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According to the parallel axiom, only one line can be drawn.
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In Euclidean geometry, the validity of the parallel axiom is essential for the structure of the geometric system.
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Many mathematicians focused on the parallel axiom to explore the differences between Euclidean and non-Euclidean geometries.
Synonyms
A rule that says there is exactly one line through a point that is parallel to a given line
Surface Forms
Morphology
The phrase is fully compositional: 'parallel' (relating to non‑intersecting lines) simply qualifies 'axiom' (a basic accepted statement), so the combination denotes an axiom concerning parallel lines. This modifier+noun pattern is a standard, cross‑linguistic way to name a specific type of axiom, so a B1 learner who knows both words can infer the MWE's general meaning (even if they may not know the formal geometric statement).
Etymology
Parallel axiom comes from a simple picture: imagine a straight line and a point not on it, then draw the one straight line through the point that will never meet the first line — that is, be parallel. So the name refers to the basic axiom, or 'rule', that there is exactly one parallel line through a point.
