Zum Stufenaufbau des Parallelenaxioms

  title={Zum Stufenaufbau des Parallelenaxioms},
  author={Victor Pambuccian},
  journal={Journal of Geometry},
Euclid's parallel postulate is shown to be equivalent to the conjunction of the following two weaker postulates: “Any perpendicular to one side of a right angle intersects any perpendicular to the other side” and “For any acute angle Oxy, the segmentPQ — whereP is a point onOx, Q a point onOy andPQ ⊥ Oy — grows indefinitely, i. e. can be made longer than any given segment”. 
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Absolute planes in which the elementary Archimedean axiom holds satisfy Aristotle’s axiom. Absolute planes satisfying both the elementary Archimedean axiom and Bachmann’s Lotschnittaxiom are


Grundlagen der Geometrie
  • G. M.
  • Mathematics
  • 1909
THIS fascinating work has long since attained the rank of a classic, but attention may be directed to this new edition, which has various additions, mainly bibliographical, and seven supplements,
Aristotle's axiom in the foundations of geometry
In the foundations of non-Euclidean geometry without Dedekind's axiom, Archimedes' axiom suffices to insure that the geometry is hyperbolic, but this axiom is not necessary. The weaker axiom of
Die Modelle des Hilbertschen Axiomensystems der absoluten Geometrie
Einleitung In dieser Arbeit soil eine Ubersicht fiber die algebraisehen Modelle des Hilbertsehen Axiomensystems der absoluten Geometric gegeben werden. Unter der absoluten Geometrie im Hflbertsehen
Zur Parallelenfrage
A statement on two circles as the geometric analog to EUCLID's field property, Bull. dcad
  • Metamathematische Methoden in der Geometrie, Springer-Verlag, Berlin,
  • 1983
A statement on two circles as the geometric analog to Euclid’s field property
  • Bull. Acad. Polon. Sci. Sér. Sci. Math., Astronom., Phys. 18
  • 1970