Pasch's axiom

proper noun

A statement in plane geometry, used implicitly by Euclid, which cannot be derived from Euclid's postulates. It states that, if a line, not passing through any vertex of a triangle, meets one side of the triangle then it meets another side.

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Meanings

proper noun
  1. geometryA statement in plane geometry, used implicitly by Euclid, which cannot be derived from Euclid's postulates. It states that, if a line, not passing through any vertex of a triangle, meets one side of the triangle then it meets another side.

Origin

Its essential role was discovered in 1882 by the German mathematician Moritz Pasch.

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Cite this entry
APA

Pasch's axiom. (n.d.). In WatkinsX Dictionary. Retrieved November 5, 2026, from https://dictionary.watkinsx.com/word/Pasch's%20axiom

MLA

“Pasch's axiom.” WatkinsX Dictionary, https://dictionary.watkinsx.com/word/Pasch's%20axiom. Accessed November 5, 2026.

Chicago

WatkinsX Dictionary, s.v. “Pasch's axiom,” accessed November 5, 2026, https://dictionary.watkinsx.com/word/Pasch's%20axiom.

Source: Pasch's axiom on Wiktionary, CC BY-SA 4.0.