...sin20) ; .-. r2 = 2a2cos 20, which is the Polar Equation. THE CYCLOID. 155. The Cycloid is described by a point in the circumference of a circle, which rolls along a horizontal line. Let BQD be the circle, О the centre ; and when its diameter is perpendicular to the...

...cylindrical spirals. The cycloid or trochoid belongs to the transcendental curves. This is described by a point in the circumference of a circle which rolls along a straight line until it has completed a revolution ; the circle, curve, and line, being supposed to continue in the...

...cylindrical spirals. The cycloid or trochoid belongs to the transcendental curves. This is described by a point in the circumference of a circle which rolls along a straight line until it has completed a revolution ; the circle, curve, and line, being supposed to continue in the...

...xuicXos and ucaf.] A geometrical curve, on which depends the doctrine of pendulums ; a figure described by a point in the circumference of a circle which rolls along an extended straight hue till it has completed a revolution. — Brandt. Cf-CLOirrAL, a. Pertaining...

...cylindrical spirals. The cycloid or trochoid belongs to the transcendental curves. This is described by a point in the circumference of a circle which rolls along a straight line until it has completed a revolution; the circle, curve, and line, being supposed to continue in the...

...y=rsin0; Л r4=2«sr8 (cos2 0-sin2 0) ; /. r>=2as cos 20. The Cycloid. 146. The Cycloid is described by a point in the circumference of a circle, which rolls along a horizontal line. Let BQD be the circle, 0 the centre ; and when its diameter is perpendicular to the...

...is called in English ealver-shaptd. Hypocycloid (Gr. !-•'', and KuirAociSif?, circular). The curve traced by a point in the circumference of a circle which rolls on the concave side of a fixed circle. When the radius of the rolling circle exceeds that of the fixed...

...It is called in English ealver-shaped. Hypocyclold (Gr. inr&, and KvK\oei5ijs, circular). The curve traced by a point in the circumference of a circle which rolls on the concave side of a fixed circle. When the radius of the rolling circle exceeds that of the fixed...

...tangent, the aris of both loci being coincident. THE CYCLOID. 92. DEF. — The Cycloid is the locus of a point in the circumference of a circle which rolls along a fixed right line. SCH. — The cycloid can be constructed mechanically by rolling a wheel, as HPI,...

...demonstration of the properties of the cycloid. The cycloid is the curve generated by the motion of a point in the circumference of a circle which rolls along a strait line. A prize had for some time been offered for the solution of the problems connected with...