Godfrey, C. (Charles), 1873-1924, Siddons, A. W. (Arthur Warry) joint author · Cambridge, University Press · leaf 151
be two eqtdcross pencils, and ifX, Y, z be coUinear, then w is on the line XYZ. … fig. 78. If W does not lie on XYZ, let PW, QW cut XYZ in A, B respectively. Then {XY, ZA} = P {XY, ZW} = Q {XY, ZW} = {XY, ZB}. XZ . AY _ XZ ■ BY ZY.XA ~ZY.XB , AY BY•• XA~XB .. A and B coincide, .•. W lies on XYZ. CROSS-RATIO 133 Theorem 56. If two equicross pencils p {abcd}, q {abcd} have a…
Geometry, Modern
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