A first course in projective geometry . Fig. 86. jlj 5. Prop. Tangents from an external point to a centralconic are eaually inclined to the focal distances of the point. Let SY, SY (Figs. 87a and b), SZ, SZ be the perpendicularsfrom the foci on the tangents from T. Then = BC- = SZ .SZ (§3 (/>)). SY _ SZSZ~STand angle YSZ = angle YSZ, each being equal to (in Fig. 87/>),or supplementary to (in Fig. 87a), the angle YTZ. .. the triangles YSZ, YSZ are similar. .. angle YZS = angleSYZ. 168 PROJECTIVE GEOMETRY But since SYTZ is cyclic, angle YZS = angle YTS in Fig. 8lh,but supplement of a
A first course in projective geometry . Fig. 86. jlj 5. Prop. Tangents from an external point to a centralconic are eaually inclined to the focal distances of the point. Let SY, SY (Figs. 87a and b), SZ, SZ be the perpendicularsfrom the foci on the tangents from T. Then = BC- = SZ .SZ (§3 (/>)). SY _ SZSZ~STand angle YSZ = angle YSZ, each being equal to (in Fig. 87/>),or supplementary to (in Fig. 87a), the angle YTZ. .. the triangles YSZ, YSZ are similar. .. angle YZS = angleSYZ. 168 PROJECTIVE GEOMETRY But since SYTZ is cyclic, angle YZS = angle YTS in Fig. 8lh,but supplement of angle YTS in Fig. 87a; and since SYTZ is. aiG. 67a. cyclic, angle SYZ = angle STZ in Fig. 87b, but supplement ofangle STZ in Fig. 87a. .. angle STY = angle STZ in both cases.
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Keywords: ., bookcentury1900, bookdecade1910, booksubjectgeometryprojective
