Smart, Edward Howard · London : Macmillian and Co. · leaf 246
>) If a, b, c, d be four fixedtangents to a conic and ]) a variabletangent, and if a, j3, y, 5 be thelengths of the perpendiculars on pfrom the points ab, be, cd, da re-spectively, then a7 = K/35, where Kis constant. (Correlative theoremdue to Chasles.) … Fig. Ilia. Let P be another variable pointon the conic (Fig. Ilia). Then we have, b}^ § 2 (a), B{APCP}=D{APCP}. . sinABP.sinCBP^sinABP.smCBP smADP.sinCDPsinADP.sinCDP . sinABP.sinCDPsinADP.sinCBP sinABP.sinCDP~ sinA D PTsinC B P sinABP.sinCDP . I.e. sinADP.sinCBP is constant. Let p be another…
Geometry, Projective
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