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Pasch's Axiom in Euclidean Geometry

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Tarski axiomatized Euclidean plane geometry in first-order logic using two primitive relations: the formula means " lies between and ", while means " is as distant from as is from ". Using , Pasch's axiom has the form

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This Demonstration illustrates the axiom.

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Contributed by: Izidor Hafner (April 2018)
Open content licensed under CC BY-NC-SA

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Reference

[1] A. Tarski, "What Is Elementary Geometry?" The Axiomatic Method with Special Reference to Geometry and Physics (L. Henkin, P. Suppes and A. Tarski, eds.), Amsterdam: North-Holland Publishing Company, 1959, pp. 16–29.

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