V there must be a third element in each of the m-classes AB, BC, CA, and by Assumption II these elements must be distinct from each other and from A, B, and C. Let the new elements be D, E, G, so that each of the triples ABD, BCE, CAG belongs to the same... Projective Geometry - Page 4by Oswald Veblen, John Wesley Young - 1910Full view
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James Roy Newman - Mathematics - 2000 - 624 pages
...that each of the triples ABD, BCE, CAG belongs to the same m-class. By Assumption III the m-classes AE and BG, which are distinct from all the m-classes...made of Assumption VII. We have, then, the theorem: * It will be noted that this test for the consistency of a set of assumptions merely shifts the difficulty...