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" This curve is generated by the motion of a point on the circumference of a circle which rolls along a right fcline. "
A Treatise on the Higher Plane Curves: Intended as a Sequel to A Treatise on ... - Page 206
by George Salmon - 1852 - 316 pages
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A Treatise on the Differential and Integral Calculus: And on the Calculus of ...

Edward Henry Courtenay - Calculus - 1855 - 526 pages
...3y2 P 9y* 3y2 (9y< Ca'y When y = 0, r = ao , and when y = oo , r = oo . 5. The cycloid, or curve generated by the motion of a point on the circumference of a circle, while the circle rolls on a straight line. Let the radius of the generating circle =: a. Place the...
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A Treatise on the Differential and Integral Calculus: And on the Calculus of ...

Edward Henry Courtenay - Calculus - 1856 - 524 pages
...parabola y2 = a?x. [l+ 6a*y When y = 0, r = ao , and when y = oo , r = . 5. The cycloid, or curve generated by the motion of -a point on the circumference of a circle, while the circle rolls on a straight line. Let the radius of the generating circle = a. Place the origin...
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A Treatise on the Differential and Integral Calculus: And on the Calculus of ...

Edward Henry Courtenay - Calculus - 1857 - 501 pages
...— ~ Q,,5* V y' + a)* When y = 0, r = x , and when y = oo , r — oo . 5. The cycloid, or curve generated by the motion of a point on the circumference of a circle, while the circle rolls on a straight line. Let the radius of the generating circle = a. Place the origin...
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A Treatise on the Higher Plane Curves: Intended as a Sequel to A Treatise on ...

George Salmon - Curves, Algebraic - 1879 - 428 pages
...commensurable with any rational number; for example, y = x v *. Here, as we successively substitute for tJ'2 the series of rational fractions which approximately...circumference of a circle which rolls along a right jline. Let A be the point where the motion commences; then (see fig. next page), in any position of...
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A Text-book on Applied Mechanics: Specially Arranged for the Use ..., Volume 1

Andrew Jamieson - Mechanical engineering - 1895 - 450 pages
...satisfy the above condition for correct working. DEFINITION. — A cycloid is a curve traced out by a point on the circumference of a circle which rolls along a straight line. The form of this curve will be understood from the accompanying figure. The rolling...
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Science and Industry, Volume 6

Industrial arts - 1901
...outlines made up of curves called epicycloidal and hypocycloidal curves. These curves are developed by the motion of a point on the circumference of a circle that is rolled on another circle. When the rolling circle ia on the outside of the other, the curve...
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A Text-book of Applied Mechanics and Mechanical Engineering, Volume 1

Andrew Jamieson - Mechanics, Applied - 1903 - 584 pages
...satisfy the above condition for correct working. DEFINITION. — A cycloid is a curve traced out by a point on the circumference of a circle which rolls along a straight line. The form of this curve will be understood from the accompanying figure. The rolling...
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A Practical Course in Mechanical Drawing for Individual Study and Shop ...

William Franklin Willard - Mechanical drawing - 1910 - 154 pages
...the rolling circle to be the end of a cylinder. Exercise 44. — Epicycloid. Fig. 44. An epicycloidal curve is generated by the motion of a point on the circumference of a circle which rolls upon a circle. Exercise 45. — Hypocycloid. Fig. 45. A hypocycloidal curve is generated by the motion...
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Monographs on Topics of Modern Mathematics: Relevant to the Elementary Field

Jacob William Albert Young - Mathematics - 1911 - 432 pages
...uninteresting to see the result which they obtained. The minimizing curve is a cycloid, that is, the locus of a point on the circumference of a circle which rolls along a straight line. In the figure the cycloid is shown inverted with its steeper part as it should be near...
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Bridge Engineering, Volume 2

John Alexander Low Waddell - Bridges - 1916 - 1140 pages
...convex curve in the vertical outline of a pilaster or of the shaft of a column. Epicycloid. — A curve generated by the motion of a point on the circumference of a circle which rolls on the convex side of a fixed circle. Epicycloidal Tooth. — See "Tooth." Equalizer. — An adjuster;...
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