Veblen, Oswald, 1880-1960, Young, John Wesley, 1879-1932 · Boston, New York [etc.] Ginn and Company · leaf 168
x=x + a, (a =£ co) or (II) x = ax, (a 4= 0) §54] LINEAR FRACTIONAL TRANSFORMATION 153 where a is the coordinate of any given point on I, each of the result-ing correspondences is projective (Theorem 2 and Theorem 4). It isreadily seen, moreover, that if x is made to correspond to (III) x=-> x… … numbers, let the line xA meet lx in X. If Y is determined as theintersection of 1X with l0) the line B Y determines on Z a point x,such that xx=l, by definition. We now have A 1 B The three projectivities (I), (II), and (III) are of fundamentalimportance, as the next theorem will show. It is…
Geometry, Projective
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