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 184
t. III.—This locus is readily sketched by drawingM N in slightly changed positions, and noting theintersections of consecutive lines, as in Fig. 166. ScH.—This locus is a variety of Hypocydoid,a kind of curve generated by a point in the cir-cumference of a circle rolling on the concave arc… … Fig. 167. Dem.—Let F[X, y, m) =0 (1), be the given locus. But from dmF(x, y, m) = 0(2), we have m = (p(x, y) ; whence the equation of the envelope becomes F{x, y, cp(x, y)} = 0 (2,). If now -^ is the same for both the locus and its en- ENVELOPES TO PLANE CURVES. 155 velope, it follows that they…
Geometry, Analytic · Calculus
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