Pasch's Axiom in Euclidean Geometry
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[more]
This Demonstration illustrates the axiom.[less]
 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.