On the stepwise construction of the parallel postulate

DOI10.1007/BF01226859zbMath0815.51012OpenAlexW2089419547MaRDI QIDQ1339785

Victor V. Pambuccian

Publication date: 8 December 1994

Published in: Journal of Geometry (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf01226859

zbMATH Keywords

absolute planeLotschnittaxiomAristotle's axiomEuclid parallel postulate

Mathematics Subject Classification ID

Absolute planes in metric geometry (51F05)

Related Items (11)

On the equivalence of Lagrange's axiom to the Lotschnittaxiom ⋮ The development of Euclidean axiomatics. The systems of principles and the foundations of mathematics in editions of the \textit{Elements} in the early modern age ⋮ Splitting the Pasch axiom ⋮ Acute triangulation of a triangle in a general setting revisited ⋮ Metric Geometries in an Axiomatic Perspective ⋮ Parallel postulates and continuity axioms: a mechanized study in intuitionistic logic using Coq ⋮ Another equivalent of the Lotschnittaxiom ⋮ Another splitting of the Pasch axiom ⋮ The elementary Archimedean axiom in absolute geometry ⋮ The ubiquitous axiom ⋮ Lippmann's axiom and Lebesgue's axiom are equivalent to the Lotschnittaxiom

Cites Work

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• Aristotle's axiom in the foundations of geometry
• Simplicity
• Die Modelle des Hilbertschen Axiomensystems der absoluten Geometrie
• Zur Parallelenfrage

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