An elementary treatise on modern pure geometry (1893)
Lachlan, Robert · London, New York, Macmillan and Co. · leaf 51
ne joining the harmonic conjugatesof P with respect to A, B; and C, D; must pass through 0and 0. Hence, if 00 meet AB in Q, Q must be the harmonicconjugate of P with respect to A and B. 62. If the pencils 0 {AB, PQ], 0 {AB, PQ] have one raycommon, i.e. if OA and OA are coincident, the three points… … Let OB, OP, OQ cut OB, OP, OQ in the points b, p, qrespectively; and let bp cut 00 in A. Then because the pencil0 [AB, PQ} is harmonic, OQ must cut the line Ab in the pointwhich is the conjugate of p with respect to ^, 6. Similarly OQmust cut Ab in the same point. Hence q the point of…
Geometry
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