On the equivalence of Playfair's axiom to the parallel postulate

Published 12 Mar 2019 in math.HO and math.MG | (1903.05233v1)

Abstract: We show that the classical equivalence of Euclid's parallel postulate and Playfair's axiom collapses in the absence of triangle congruence. In particular, we construct a non-SAS geometry that models the Playfair axiom but not the parallel postulate.

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