Veblen, Oswald, 1880-1960, Young, John Wesley, 1879-1932 · Boston, New York [etc.] Ginn and Company · leaf 188
(1) Oaoox== Occjb. m A n y Hence we have (2) »(-io,floo.)=»(-io,oo^, which, when expanded (Theorem 13, Chap. VI), gives for the desiredcondition (3) ma + nl + 1 = 0. This condition has been shown to be necessary. It is also sufficient,for, if it is satisfied, relation (2) must hold, and hence would… … Fig. 81 If now a = 0 (b =t= 0), we have at once b = — 1/n ; and if b = 0 (a #= 0),we have likewise a = — 1/m for the condition that P be on I. Buteach of these relations is equivalent to (3) when a = 0 and b = 0respectively. The combination a = 0, b = 0 gives the origin 0 whichis never on a line…
Geometry, Projective
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