Elements of analytical geometry and the differential and integral calculus (1856)
Robinson, Horatio N. (Horatio Nelson), 1806-1867 · Cincinnati : J. Ernst · leaf 257
n of the evolute. (dx^-\-dy) f—h-. dy dx\ d^y / The values of dx, dy, and d^y, substituted in these equationsand reduced, the results will be Whence and X—a=—2j2ryy=—hf and ;r=a -y^- 2j2ry—y^. The first of these equationsshow that QMz=PM. Thelast article demonstrated thatMN=NM, therefore the… … TRANSCENDENTAL CURVES. 249 If the value of x and y be taken from the last equation andsubstituted in the geometrical equation of the cycloid, we shallhave, after a little reduction, a=arc(sin.=(7—2r6—^2)—^—2r6—62, (1) the equation of the evolute AMA. To make this equation more clear, we will…
Geometry, Analytic · Calculus
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