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 183
^» » SECTION YIIL Envelopes to Plane Curves. 230. Def.—An JEnvelope is the locus of the intersection ofconsecutive lines, or curves, represented by a given equation, whenone or more of its parameters are made variable. III.—Let {x — w)2 -j- j/^ — r2 — 0 be the equation of the locus whose envelope… … Fig. 163. N is required. Let m be the (variable)parameter. Let r = Bl, so that Baashall be one position of the given locus,which in this case is a circle. Now sup-pose m to take an infinitesimal incre-ment dm, putting the centre at 2, and giving {x — (m -f- dm)}^ + 2/^ — r^ = 0as the equation of…
Geometry, Analytic · Calculus
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