Plane and solid analytic geometry; an elementary textbook (1904)
Ashton, Charles Hamilton, 1866-1936 · New York, C. Scribner's Sons · leaf 217
re invented. 200 ANALYTIC GEOMETRY [Ch. XV, § 10/ 105. The cycloid.—The path described by a point onthe circumference of a circle which rolls on a straightline is called a cycloid. Let C be the centre of the moving circle of radius a,and let P be the fixed point on its circumference. Tofind the… … Fig. 103. parallel to the same line. Let 6 represent the circular measure of the angle MCP through which the radius CP has revolved. Let the coordinates of P be (x, y). Then x = OM- PK, and y = MC - KC. But 0M= arc MP = a0, PK= PC sin 0, and KC = PC cos d. Hence x — a (6 — sin 0), y = a(l — cos 0).…
Geometry, Analytic
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