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Pasch's axiom

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.

Proper noun

Pasch's axiom

  1. 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.

Origin of Pasch's axiom

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

Questions about Pasch's axiom

What does Pasch's axiom mean?
Pasch's axiom means 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.
What part of speech is Pasch's axiom?
Pasch's axiom is a proper noun.

Words near Pasch's axiom in the dictionary

  1. Pascarella
  2. pasch
  3. Pasch egg
  4. Pasch eggs
  5. Pasch of the Cross
  6. Pasch's axiom
  7. Pasch's theorem
  8. Pascha
  9. Pascha egg
  10. Pascha eggs
  11. paschal

Source and license

Adapted from Wiktionary: Pasch's axiom (page history and authors). Text available under the Creative Commons Attribution-ShareAlike 4.0 license. Word.ws reformatted the entry and added links. Wiktionary data of 2026-09-02.

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