 | John Farrar - 1825 - 492 sivua
...pass now to the consideration of the centre of gravity of plane surfaces bounded by curved lines. 104. Let it be required to find the centre of gravity of the Fig. 42. surface APM; and let G represent this centre. In order to obtain the distance GG', it is necessary... | |
 | Thomas Curtis - 1829 - 822 sivua
...= fluent т xx , . n г • MN — ^== rz r, whence А О — r гчтJîru — i? AM Example 3.— r T. Tegg segment of a sphere ? In this case fluent \fxi fluento.r — fluent y* i 4 o — 3x fluent ax — x*... | |
 | Isaac Todhunter - 1853 - 362 sivua
...the slice parallel to that of (x, y}j and the edges of the strip parallel to the axis of x. 129. Ex. Let it be required to find the centre of gravity of the solid bounded by the planes x = 0, y = 0, z = /3a;, z = 70:, and the cylinder y* = 2ax - x'. We shall... | |
 | Thomas Tate - 1853 - 396 sivua
...gravity, and c the centre of the circle ; then, radius CD x chord DE ,, v CG= - — . . . (1). arc DE (1.) Let it be required to find the centre of gravity of the sector ABC. Conceive the sector to be divided into an infinite number of triangles, by lines drawn... | |
 | Isaac Todhunter - 1866 - 386 sivua
...the slice parallel to that of (a;, y), and the edges of the strip parallel to the axis of x. Ex. 2. Let it be required to find the centre of gravity of the solid bounded by the planes z = fix, z = yx, and the cylinder y2 = 2ax — x2. We shall have III xdxdydz... | |
 | William John Macquorn Rankine - 1872 - 714 sivua
...(which will be given in the sequel) for finding the centre of gravity of a sector of a circular disc, and let it be required to find the centre of gravity of a sector of an elliptic disc. In fig. 27, let A B' AF be the ellipse, AOA = 2 a, and B' O B' = 2 b,... | |
 | William John Macquorn Rankine, Edward Fisher Bamber - 1873 - 368 sivua
...supposed that the centre of gravity of a sector of a circular disc has been found (Case IX. Article 44), and let it be required to find the centre of gravity of a sector of an elliptic disc. In fig. 99, let A B' A B' be the ellipse, AOA = 2 a, and B' O B' = 2... | |
 | William John Macquorn Rankine, Edward Fisher Bamber - 1873 - 372 sivua
...supposed that the centre of gravity of a sector of a circular disc has been found (Case IX. Article 44), and let it be required to find the centre of gravity of a sector of an elliptic disc. In fig. 99, let A B' A B' be the ellipse, AOA = 2 a, and B- O B' = 2... | |
 | George Minchin Minchin - 1877 - 470 sivua
...OCioaf = OD. As an example, let the curve AB be a quadrant of a circle of which OA and OB are diameters, and let it be required to find the centre of gravity of the solid hemisphere generated by the revolution of this quadrant round OB (taken as axis of#), firstly... | |
 | Robert Hudson Graham - 1883 - 478 sivua
...GRAVITY. 149 duced in a certain ratio. —. — -' — r. beyond the sides of an equiangular polygon, 1, 2, 3, 4, . . 7, 8. Let a series of equally heavy particles...example to that drawn perpendicularly to the side, 8. Let the radius-vector, 0 A, of the point, A, equal, c ; and let the angle, A()X — a. If the polygon... | |
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Article 44), and let it be required to find the centre of gravity of a sector of an elliptic disc. In fig. 99, let A B' A B' be the ellipse, AOA = 2 a, and B' O B' = 2 b, its axes, and 0' O D' the sector whose centre of gravity is required. 
