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SPACES OF DIMENSION THREE WITH CONGRUENCE

It is well known that every Euclidean plane (E, L, α, ≡) is isomorphic to an affine plane A G(2,K) over a Pythagorean ordered commutative field K . There is a corrisponding theorem for hyperbolic panes (cf. [2]). For both proofs one first considers the group of motions, in particular the line reflections.