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 181
to theevolute, the point of tangency is the centre of curvature, and consequentlythe normal thus produced is the radius of curvature. Dem. —Let (m, n) be any point in the evolute of AIVI,from it draw a normal to AM, and let {X, y) be thepoint at which it is normal. The equation of this nor- mal is… … Fig. 160. dx — dm -{- dy- — dndy dx + {y ^^df = « or ^+1:+*^ dy dmdx- dx dx dndy dx^ = 0. (2) But as (m, n) is in the evolute we have {208) yd^y dydx^ whence ^ + % + y n) dx-^ dmdx 0. Therefore dropping these terms, (2) becomesdn dy dx^dxdy dxdy dn dm = 0, and {X — m), which is the equation of a…
Geometry, Analytic · Calculus
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