# Pasch's Axiom in Euclidean Geometry

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

β(XYZ)

Y

X

Z

δ(XYZU)

X

Y

Z

U

β

(∃V)(β(XTU)∧β(YUZ)⇒β(XVY)∧β((ZTV))

This Demonstration illustrates the axiom.