Woods, Frederick S. (Frederick Shenstone), 1864-, Bailey, Frederick H. (Frederick Harold), 1865- · Boston, New York [etc.] Ginn and Company · leaf 126
onstant rate along the auxiliary circle ofan ellipse; required the motion of its accompanying point P.As in § 53, <f> = —■ Hence the equations of the path are kt y bsm It THE CYCLOID 109 55. The cycloid. If a circle rolls upon a straight line, eachpoint of the circumference describes a curve… … Fig. 93 describes the cycloid. Take as the origin of coordinates, 0, thepoint found by rolling the circle to the left until P meets OX. Then ON= arc IX. Draw MP and CX, each perpendicular to OX, PR parallel toOX, and connect C and P. Let angle X(P= <f>.Then x = OM = OX - MN = arc XI-PR= a…
Geometry, Analytic · Calculus
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