Veblen, Oswald, 1880-1960, Young, John Wesley, 1879-1932 · Boston, New York [etc.] Ginn and Company · leaf 157
ration o on a pair of points A, B is meant any processwhereby with every pair A, B is associated a point C, which is unique providedthe order of A, B is given; in symbols AoB = C. Here order has no geo-metrical significance, but implies merely the formal difference of AoB and Bo A.IfAoB = BoA, the… … Theorem 1. If Px and Py are distinct from P0 and Px>,Q(P0OPxPQ,PxPyPx+y) is a necessary and sufficient condition for the equalityP* + Py = Px+r (A,E) This follows immediately- from the definition, AXAY being aquadrangle which determines the given quadrangular set. Corollary 1. If Px is any point…
Geometry, Projective
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