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Pasch's axiom

Not to be confused with Pasch's theorem.

In geometry, Pasch's axiom is a statement in plane geometry, used implicitly by Euclid, which cannot be derived from the postulates as Euclid gave them.[1] Its essential role was discovered by Moritz Pasch in 1882.[2]

  1. ^ It can, however, be derived from weaker axioms of plane separation taken for granted by Euclid, as shown in Pambuccian 2024
  2. ^ Pasch 1912, p. 21

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