Elements of analytical geometry and the differential and integral calculus (1856)
Robinson, Horatio N. (Horatio Nelson), 1806-1867 · Cincinnati : J. Ernst · leaf 88
when at A or A, PF and PFwill be two sides of a triangle, and the diflference of these twosides is constantly equal to the difference between the ruler andthe thread ; but that difference was made equal to the given lineAA ; hence, by Def. 1, the curve thus described must be anhyperbola.… … I ANALYTICAL GEOMETRY. Now we have two right angled triangles, PHF and PHF\By the definition of the curve we have /~-r=:2^. (1) The right angled A PSF gives r2=(ar—c)2+y^ (2) The right angled A PHF gives /2^(^_|.,)2^2/^ (3) Subtracting (2) from (3) produces Dividing (4) by (1), and we have /+r=?^.…
Geometry, Analytic · Calculus
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