On a splitting of the parallel postulate

Research output: Contribution to journalArticlepeer-review


While the Euclidean parallel postulate P can be replaced with the conjunction of the two axioms, “Given three parallel lines, there is a line that intersects all three of them” (ML) and “Given a line a and a point P on a, as well as two intersecting lines m and n, both parallel to a, there exists a line g through P which intersects m but not n” (S) to obtain plane Euclidean geometry based on Hilbert’s plane absolute geometry A, it is shown if A is slightly weakened, in the sense that either the order axioms are weakened or a congruence axiom is weakened, then the conjunction of ML and S is no longer equivalent to P.

Original languageEnglish (US)
Article number12
JournalJournal of Geometry
Issue number1
StatePublished - Apr 2022


  • Lotschnittaxiom
  • metric-Euclidean planes
  • ordered geometry
  • Parallel postulate

ASJC Scopus subject areas

  • Geometry and Topology


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