Abstract
In these T r a n s a c t i o n s, vol. 3 (1902), p. 14S, E. H. MOORE has given a set of projective axioms for geometry. In further development of the standpoint of MOORE a system of axioms for three dimensional Euclidian geometry has been constructed by VEBLENt by means of the betweenness relation. :X: A feature of VEBLEN'S system is that a planar axioln (axiom VIII, l. c.) is necessary to establish the existence of an infinitude of points and to prove the theorem, To any four distinct points of a line the notation A, B, C, D may always be assigned so that they are in the order ABCD. In this note I give a set of independent axioms in terms of sameness of sense of dyads, abstractly expressed by a,liK¢y8§, which implies VEBLEN'S axiotns I-VIII, but which does not require a planar axiom for the proof of the precteding propelties. Of the two relations, sameness of sellse and betweenness, one is definable in terms of the other; but the two definitions are not equally simple, as will appear below. §2.
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