Elements of analytical geometry and the differential and integral calculus (1856)
Robinson, Horatio N. (Horatio Nelson), 1806-1867 · Cincinnati : J. Ernst · leaf 249
ation of the curve. Let AF=r, then we must designate the arc BD by i, and theproportion will be the same as before, and so on for any point inthe curve. When AB has made one revolution, then^=2a7t, and the equa-tion becomes r=l, corresponding with the construction. The equation shows thatr cannot… … TRANSCENDENTAL CURVES. 241 On the other hand, when t is very small, r will be correspond-ingly great; hence, the curve, after passing N, will run off andbecome nearly parallel to AB, and in that sense AB is an asymp-tote to the curve, and hence the name hyperbolic spiral. The two preceding spirals,…
Geometry, Analytic · Calculus
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