Elements of analytical geometry and of the differential and integral calculus (1866)
Davies, Charles, 1798-1876 · New York, Barnes & Co. · leaf 378
describe the involutecurve. Evolute of the Cycloid. 152. Let us resume the equation for the radiujs of curv-ature (Ait. 141), M = - (^!_tjW .... (, dxa-y ^ If, in this equation, we substitute the value of dx andd^y., found in Art. 113, we have, E = ^{njY = 2^2^^. . . . (2.) hence (Art. Ill), The… … If, in Equation (2), we make y = 0, we have, BIf we make y — MB — 2r, we have, It = ir. Tliat is, the radiusof curvature is zero atthe point A, and twicethe diameter of thegenerating circle at B. Since the radius ofcurvatlire and evoluteare both zero at thepoint A, and since theyincrease equally…
Geometry, Analytic · Calculus
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