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 180
e evolute is a point, the centre. This is evidently correct,since all normals (radii) of the circle meet at the centre. 150 PROPEBllES OF PLANE LOCI. Ex. 3. Find the evolute of the ellipse. Sugs.—We have m = ——, n = — ^, and A^y^A-B^x^A^ B^ = A^B\ from which to eliminate x and y and find an… … dy \/2ry—■//-dx y dry dx^ Stjgs. —We have ^:= -■^——, and ^j—; = -,. Whence m=x-\-2\/2ry—y% and n= — y. .-. y = — n, and x = m — 2 v/— 2ni — rv^. Substituting thesethe equation of the cycloid, we have m = vers—^(— n)-\-\^ — 2rn — v!^. ui 22S, CoR.—The evolute of a cycloid is an equal cycloid. Yj A E…
Geometry, Analytic · Calculus
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