Schmall, Charles Nelson. [from old catalog] · New York, D. Van Nostrand company · leaf 265
= aO — a sin 0 = a {0— sin 0)Similarly, y = a {1 — cos 0) . . . To eliminate 6, we get from (2), cos 6 a-y Also, sin 0 ± V2 ay -y^ (1)(2) . = cos-.(^).vers-.(|); Substituting these values in (1), we obtain X = a vers~i — — V2 ay - y% which is the required equation of the cycloid. Note. — Equations… … Fig. 141. To find its equation: Take 0, the center of the fixed circle,as origin, and the ± diameters OAX, OY, as axes. Let A bethe initial point of the curve. Radius of fixed circle = a ) . m>Ti — a. Radius of moving circle = 6 j — v>- HIGHER PLANE CURVES 249 Let P (x, y) be any point on the…
Geometry, Analytic
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