Elements of analytical geometry and the differential and integral calculus (1856)
Robinson, Horatio N. (Horatio Nelson), 1806-1867 · Cincinnati : J. Ernst · leaf 62
cholium 2. To find NR, the subnormal^ we simply subtractCiVfrom CR, whence NR=x^(^!:^l\x^=^.\ A^ / A^ We can also find the subnormal from the proportional trianglesFRT, PNR, thus: TR : RP :: RP : RN. ~:^LI._ : y :: y : —NR. Whence iV72=_^. PROPOSITIOl^ VIIL Z^w^s drawn from the foci to any point in… … CF=JA^—B^ by c, CF by ~c, the angle FPT by F, andthe tangents of the angles PTX, PFT, by a and a. Now FPT=zPTX-—PFT. By trigonometry, (Eq. 28, p. 143, Robinsons Geometry), wehave Tan. FPT=tsLn.(PTX—PFT). That is, tan. V=-II^. (1) l-\-aa Prop. VI, gives us a—— x\ y\ being the co-ordi- A^y nates of…
Geometry, Analytic · Calculus
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