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In his paper Sets of metrical hypotheses for geometry,] R. L. Moore raises the question whether the set O of order axioms and the set C of congruence axioms employed therein, together with M, the proposition that every segment has a mid-point, and P 2 , a form of the parallel postulate, are sufficient to give the semi-quadratic geometry of a three-space. At the same time, he states that this question may be answered in the affirmative if it can be proved on the basis of O, C, and M that all right angles in space are congruent to each other. In the present paper it will be shown that O and C are sufficient to require that all right angles in space be congruent to each other. It is a result of a recent paper $ of the present author that the theorems of sections 1,2,3, and 4 of M.H. are consequences of O and C. Theorems from these sections of M.H. will be quoted without further mention of this justification of their use.

Concerning a set of axioms for the semiquadratic geometry of a three-space