 | George Salmon - Conic sections - 1852 - 338 pages
...commensurable with any rational number ; for example, y = X12. Here, as we successively substitute for y' 2 the series of rational fractions which approximately...A be the point where the motion commences ; then, in any position of the generating circle, if p be the generating point, we must have the arc pm = Am,... | |
 | 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 - Mathematics - 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 - 522 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 - 426 pages
...able to find that, even in this case, the discriminant is expressible in terms of lower invariants. CHAPTER VII. TRANSCENDENTAL CURVES. 303. WE have hitherto...circumference of a circle which rolls along a right fcline. Let A be the point where the motion commences ; then (see fig. next page), in any position... | |
 | 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... | |
 | Andrew Jamieson - Mechanical engineering - 1895 - 448 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... | |
 | Science - 1901 - 678 pages
...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 - 156 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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This curve is generated by the motion of a point on the circumference of a circle which rolls along a right fcline. 
