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Common to the two geometries is only the general property of one-to-one correspondence, and the rule that this correspondence determines straight lines as shortest lines as well as their relations of intersection.

Hans Reichenbach (1958). “Philosophie Der Raum-Zeit-Lehre”, p.90, Courier Corporation
Common to the two geometries is only the general property of one-to-one correspondence, and the rule that this correspondence determines straight lines as shortest lines as well as their relations of intersection.