 | Bartholomew Price - Calculus - 1854 - 592 pages
...angle t to the semi-axis whose length is (\2-^),, ^ ^ (gjni)' (cos t)2 rf» ~ X2-n»+ X^2' also if p be the perpendicular from the centre of the ellipsoid on the tangent plane at (/n, v), by Art. 164, 1 (\«since, then, p* = v 2 (sin i)2 + fA2 (cost)2, and therefore pd = a. constant... | |
 | Bartholomew Price - Calculus - 1854 - 590 pages
...(22), Art. 133, if ds represent the infinitesimal surface-element, ds = (135) But if p = the length of the perpendicular from the centre of the ellipsoid on the tangent plane, and therefore ai>c tin 0 de d da = - : P and if s = the whole surface of the ellipsoid, s = abcj... | |
 | Percival Frost - Geometry, Analytic - 1875 - 458 pages
...— _£_ (», (6) A point moves on an ellipsoid so that its direction of motion always passes through the perpendicular from the centre of the ellipsoid on the tangent plane at the point; shew that the curve traced out by the point is given by the intersection of the ellipsoid... | |
 | Charles Smith - Geometry, Analytic - 1884 - 256 pages
...of the curve 4. A point moves on an ellipsoid so that its direction of motion always passes through the perpendicular from the centre of the ellipsoid on the tangent plane at any point ; shew that the curve traced out by the point is given by the intersection of the ellipsoid... | |
 | Charles Smith - Geometry, Analytic - 1886 - 268 pages
...— XT ^ y , 4. A point moves on an ellipsoid so that its direction of motion always passes through the perpendicular from the centre of the ellipsoid on the tangent plane at any point ; shew that the curve traced out by the point is given by the intersection of the ellipsoid... | |
 | George Chrystal, Napier Shaw - Electricity - 1894 - 224 pages
...mass of the shell is fapd(a.bc) — i-rfiiibcp, therefore Q — j — , ^ Also в = рр where p is the perpendicular from the centre of the ellipsoid on the tangent plane. Whence we get 4*abc (Щ; 2 2 VrV,r-ll^l " '( Elli soW ' ' The energy supplied from without is t { 2(... | |
 | Sir George Greenhill - Hydrostatics - 1894 - 568 pages
...through any angle. Prove that the work necessary to effect the displacement varies as a—p, where p is the perpendicular from the centre of the ellipsoid on the tangent plane parallel to the new surface of the water, and 2a the longest axis. OH O 210 NUMERICAL CALCULATIONS... | |
 | Encyclopedias and dictionaries - 1907 - 798 pages
...mass of the shell is frpd(aoc) — 4*цаЬср, therefore Q — A4*jiabcp. Also 9 — мр where p is the perpendicular from the centre of the ellipsoid on the tangent plane. Whence we get JT\_ (M) 4.0&C that is, the density at any point varies directly as the distance of the... | |
 | J. V. Armitage, W. F. Eberlein - Mathematics - 2006 - 9 pages
...b2 c2 where a, b, c are not all equal, and for simplicity we shall suppose a > b > c. We denote by/? the perpendicular from the centre of the ellipsoid on the tangent plane at the point (x, y, z), and then if cos a, cos ft and cos y denote the direction cosines of the normal... | |
| |
A point moves on an ellipsoid so that its direction of motion always passes through the perpendicular from the centre of the ellipsoid on the tangent plane at any point ; shew that the curve traced out by the point is given by the intersection of the... 