Elements of analytical geometry and the differential and integral calculus (1856)
Robinson, Horatio N. (Horatio Nelson), 1806-1867 · Cincinnati : J. Ernst · leaf 94
uation to Whence x= ^d!±:?!^a;= CK If we subtract CD, («), from CiV, we shall have DN, thestib-normal. That is, /A^-{-B^\ ._^.^ ■^ t^e sub-n&rmal \ A^ / A THE HYPERBOLA.PROPOSITION VI. 85 A tangent to the hyperbola bisects the angle contained hy linesdravmfrom the point of coniact to the foci.… … exA _A^ X (2) FT==FC-\-CT=c+--, and TF=c- X We will now assume the proportion Multiply the first couplet by A, and the last couplet by x,then we shall have {A-\-cx) : {—A-\-cx) : : {cx-^-A) : xz.Observing that the first and third terms are equal, thereforexz-=^cx—A^.A Or ;—__=ri^. Now the first…
Geometry, Analytic · Calculus
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