Smart, Edward Howard · London : Macmillian and Co. · leaf 272
he polar of P with respect to the conic passes through Othe point of intersection of AA and BB (Chap. VIII. ^ 7 (VIII.)),also through K the point of intersection of the tangents at Xand Y (def. of polar). .. it is KO. .. the pencils K(PXOY), O(PAKB) are harmonic, and conse-quently homographic. But… … Fig. 124. But since K{PXOY} is harmonic, by the property of thecomplete quadrilateral, KO passes through the intersection ofXR and YQ. It follows, by the converse of Brianchons Theorem, that aconic can be drawn touching KX and KY at X and Y, and also AAand BB (ROQXKY is the Brianchon hexagon).…
Geometry, Projective
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