# The Ubiquitous Axiom

@article{Pambuccian2021TheUA, title={The Ubiquitous Axiom}, author={Victor Pambuccian and Celia Schacht}, journal={Results in Mathematics}, year={2021}, volume={76}, pages={1-39} }

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…

## 2 Citations

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(Hartshorne, 2000) interprets Euclid’s Elements provides an interpretation of Euclid’s Elements in the Hilbert system of axioms, specifically propositions I.1-I.27, covering the so-called absolute…

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