The Ubiquitous Axiom

  title={The Ubiquitous Axiom},
  author={Victor Pambuccian and Celia Schacht},
  journal={Results in Mathematics},
This paper starts with a survey of what is known regarding an axiom, referred to as the Lotschnittaxiom, stating that the perpendiculars to the sides of a right angle intersect. Several statements are presented that turn out to rather unexpectedly be equivalent, with plane absolute geometry without the Archimedean axiom as a background, to the Lotschnittaxiom. One natural statement is shown to be strictly weaker than the Lotschnittaxiom, creating a chain of four statements, starting with the… 
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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,
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