 | George Salmon - Conic sections - 1852 - 329 pages
...curves, both for historical interest and for the variety of its physical applications. This curve is generated by the motion of a point on the circumference of a circle which rolls along a right line. Let A be the point where the motion commences; then, in any position... | |
 | George Salmon - Conic sections - 1852 - 338 pages
...curves, both for historical interest and for the variety of its physical applications. This curve is generated by the motion of a point on the circumference of a circle which rolls along a right line. Let A be the point where the motion commences ; then, in any position... | |
 | Edward Henry Courtenay - Mathematics - 1856 - 524 pages
...also. . 4. The cubical 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...Place the origin at V, the vertex of the cycloid. 1'nt VD — x, DP — y, the point P being that which describes the curve APVB, while the circle rolls... | |
 | Edward Henry Courtenay - Calculus - 1857 - 522 pages
...- 3"2 • 2.y _f!l _ 2a* •^ ~ 3u2"i -P ~ ~ oTl :i,/2 — ~ Q,,5* V y' + a»)* When y = 0, r = x , and when y = ± oo , r — oo . 5. The cycloid, or...Put VD =: x, DP = y, the point P being that which deseribes the curve AP FT?, while the circle rolls on the line ACB. Then PD — DF + FP = DF + EC since... | |
 | Edward Henry Courtenay - Calculus - 1860 - 516 pages
...diilus. 号 ( 9y4 十" 4 ) 6"4y 45 ㏄Ⅴ 29 / = ０ ，グニの，ゐ℡ dWhen ツ=士の)グニの。 5. The cycloid, or curve generated by the motion of...circle rolls on a straight line. Let the radius of the generat ing circle @ a. Place the origin at F, the vertex of the cycloid. Put VD = a?, DP = y, the... | |
 | Edward Henry Courtenay - Calculus - 1868 - 530 pages
...oo ; and when y = oo , r = » also. 4. The cubical parabola y3 = a?x. 3y2 3a2 . 2y 9y 2a« 'V* 9y5 When y = 0, r = ao , and when y = ± oo , r = oo ....y, the point P being that which describes the curve AP VB, while the circle rolls on the line ACB. Then PD — DF + FP = DF + EC since EP and CF are parallel.... | |
 | Edward Henry Courtenay - Calculus - 1873 - 528 pages
...— - = - — . «У »У «У "y (9у« + а4)1 !¿a* (ki4y When у = 0, r = ao , and when у = ± oo , r = oo . 5. The cycloid, or curve generated by...y, the point P being that which describes the curve AP VB, while the circle rolls on the line ACB. Then PD — DF + FP = DF + EC since EP and CF are parallel.... | |
 | Edward Henry Courtenay - Calculus - 1873 - 524 pages
...P О, л ' 'J..2 '¿у2 ч6а«у 9? When у = 0, г — оо , and when у = ± ао , г = а> . 5. The cycloid, or curve generated by the motion of...y, the point P being that which describes the curve AP Vß, while the circle rolls on the line ACB. Then PD — DF + FP — DF + EC since JSP and OF are... | |
 | 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... | |
 | William Franklin Willard - Mechanical drawing - 1910 - 156 pages
...facing stones radiate from their respective centers. Fig. 42. Exercise 43. — Cycloid. Fig. 43. A curve generated by the motion of a point on the circumference of a circle which rolls on a straight line is called a cycloid. The figure clearly illustrates the construction.... | |
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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 origin at... 
