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Sets of metrical hypotheses for geometry

1908
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Transactions of the American Mathematical Society
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In this paper is given a set of assumptions, C, concerning point, order f and congruence, which, together with a certain set of order assumptions 0,% a continuity assumption F,% and a very weak parallel assumption P0,% are sufficient for the establishment of ordinary Euclidean geometry. Each assumption of this set is independent of all the remaining ones. Moreover congruence is here an independent symbol in the sense that it would be impossible § to prove that if the order assumptions 0, TTand

doi:10.1090/s0002-9947-1908-1500823-x
fatcat:pdpyhwfbmja5jghy2srwi7od3i