Smart, Edward Howard · London : Macmillian and Co. · leaf 153
erhaps the most usefulof these is (the so-called) Newtons theorem, which may beenunciated as follows: If chords be drawn through any point in the plane of aconic to meet the curve, the ratio of the rectangles of theirsegments depends only upon the directions in which thechords are drawn, not upon… … Fio. 63. Let w, %d be the infinitely distant points of intersectionof the parallels, and let qtl meet PP at \i and fp meet QQat 11. Then, applying Carnots theorem to the triangle tuw^ uq. uq t]). tp tvP. wPtq . tq urp . wp uP. uP But wP = v:^ and wP = top. . tp. ip _ wP. uPtq.tci uq . u^ 126…
Geometry, Projective
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