Smart, Edward Howard · London : Macmillian and Co. · leaf 241
formed bytheir four conjugates. (h) The intersections of fourfixed tangents to a conic withany fifth tangent form a rangeof constant cross-ratio. § 2. Props, (a) The joinsof four fixed points on a conicto any fifth point on the curveform a pencil of constant cross-ratio. We shall prove the theorems… … Then Fig. 107a. sin AVB . sin CVD VJABCD} =^—--T^r,^ ^ sm AVD . sni CVB and the angles AVB, CVD, AVD, CVB are either equal or supplementary to the angles AVB, CVD, AVD, CVB. In either case the sines of these angles are equal each toeach. Hence V{ABCD} =V{ABCD}, and theorem (a) is proved forthe…
Geometry, Projective
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