An elementary treatise on modern pure geometry (1893)
Lachlan, Robert · London, New York, Macmillan and Co. · leaf 295
ivith the pencil formed by the polars of the points withrespect to a circle. Let A, B, C, D be any four collinear points, and let PA, PB,PC, PB be the polars of A, B, G, D, with respect to a circle whosecentre is 0. Then, since the lines PA, PB, &c., are perpendicular 278 THEOREMS RELATING TO… … Let AEC be the conjugate triangle of ABC; and let the correspondingsides intersect in the points X, T, Z. Then, if jBC cut ABvn the point D,the point D will be the pole of AC. Also X is the pole of AA. Thereforeby § 431, the range {BX, DC) is equicross with the pencil A{YA\ CB}.But, {BX, I)C} =…
Geometry
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