| 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... | |
| 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... | |
| 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... | |
| George Salmon - Curves, Algebraic - 1879 - 424 pages
...commensurable with any rational number ; for example, y = xv*. Here, as we successively substitute for **\/2 the series of rational fractions which approximately...Let A be the point where the motion commences ; then** (see fig. next page), in any position of the generating circle, if p be the generating point, we must... | |
| George Salmon - Curves, Algebraic - 1879 - 424 pages
...commensurable with any rational number ; for example, y = x**. Here, as we successively substitute for **\/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... | |
| 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... | |
| 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... | |
| 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... | |
| 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... | |
| 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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