# Pieri's Ternary Relation and Euclidean Geometry

Pieri's Ternary Relation and Euclidean Geometry

M. Pieri showed that the ternary relation of a point being equally distant from two other points (in symbols, ) can be used as the only primitive notion of Euclidean geometry of two or more dimensions [1]. This Demonstration shows Robinson's definition of the quartic relation

AB=BC

AB≤BC⇔∀X(BX=XC∃Y(AY=YB=BX))

in terms of Pieri's relation. This relation can be used to define relations that a point is between and ; that , , are collinear; and that is the midpoint of .

B

A

C

A

B

C

B

AC

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