. An elementary treatise on the differential calculus founded on the method of rates or fluxions. Prolate cycloid. of the curve are x — aip — b sin ipy — a — b cos if) (1) When b a, the cur-tate cycloid. Fig. Curtate cycloid. Examples. 1. Show that the curtate cycloid cuts the axis of x at right angles,and, in general, that the line RP is perpendicular to the tangent tothe trochoid at P. 2. Determine the points of inflexion in the prolate cycloid. Showthat at the point of inflexion the radius of the generating circle is tan-gent to the curve. , b ib = cos-1— . d\ . a To find —4 in terms o
. An elementary treatise on the differential calculus founded on the method of rates or fluxions. Prolate cycloid. of the curve are x — aip — b sin ipy — a — b cos if) (1) When b a, the cur-tate cycloid. Fig. Curtate cycloid. Examples. 1. Show that the curtate cycloid cuts the axis of x at right angles,and, in general, that the line RP is perpendicular to the tangent tothe trochoid at P. 2. Determine the points of inflexion in the prolate cycloid. Showthat at the point of inflexion the radius of the generating circle is tan-gent to the curve. , b ib = cos-1— . d\ . a To find —4 in terms of tj\ use the method exemplified in Art. 289. § XXXL] THE EPICYCLOID. 313 The Epicycloid. 293. When a circle, tan-gent to a fixed circle exter-nally, rolls upon it, the pathdescribed by a point in thecircumference of the rollingcircle is called an epicycloid. Taking the origin at thecentre of the fixed circle,and the axis of x passingthrough A, (one of the posi-tions of P when in contactwith the fixed circle,) a, b, tp,and Xj being defined by thediagram, we have, evidently,
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