A first course in projective geometry . >) 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}. ^ . ~ sinA D PTsinC B P . is constant. Let p be another variable t
A first course in projective geometry . >) 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}. ^ . ~ sinA D PTsinC B P . is constant. Let p be another variable tan-gent to the conic (Fig. 1116), Then we have, by § 2 (6), b {apcp } = d{ apcp}. Lettering the angular points,this gives ~ Hence gP^^ BK^a, is constant. PROPERTIES OF THE CONIC 219 ^ sinABP _ a/BP _ asinCBP~/3/BP~/3 Similarly sinCDP_7sinADPS — is constant. But 7STs= and -jr^^ = 7 AQ a ^ is
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