A general geometry and calculus : including book I. of the general geometry, treating of loci in a plane; and an elementary course in the differential and integral calculus (1881)
Olney, Edward, 1827-1887 · New York : Sheldon and Co. · leaf 173
in, let s represent thelength of the curve, and tp, the angle at thecentre of the osculatory circle to radiusunity. As P and P are consecutive points,PP = ds, PL = (ix, P L = dy, and ce =dip are contemporaneous infinitesimal elements of s, x, y, and tp respectively.Moreover, drawing EH parallel to… … Fig. 151. -^ ) is the angle a normaldy / makes with the axis of x. Now since cethe centre, and PP = ds, is the corresponding arc at r from the centre, we have ds df the — sign signifying that s is a decreasing (1) ds = — rdip, or r =function of tp. But ds = ±: \/dy^ -j- dx^; and differentiating…
Geometry, Analytic · Calculus
Internet Archive · Boston College Libraries · Public Domain Mark 1.0. Free to use for anything.
