 | Duncan Farquharson Gregory - 1845 - 364 pages
...contact. The equations to the normal at the point x, y, z are, by equation (10) of Art. (161), y If p be the length of the perpendicular from the centre, on the tangent plane, we have hy equation (16) of Art. (164) To find the locus of the intersection of the tangent plane with... | |
 | Duncan Farquharson Gregory - Geometry, Analytic - 1845 - 308 pages
...equation (10) of Art. (161), a2 (x' - x) _Jf (y1 - y) _ <? (z - z) x у z TANGENTS TO SURFACES. If p be the length of the perpendicular from the centre, on the tangent plane, we have by equation (16) of Art. (164) To find the locus of the intersection of the tangent plane with... | |
 | George Salmon - Conic sections - 1855 - 376 pages
...half the angle between the asymptotes = - ; therefore, if this angle = 45°, we have 6 = a. 179. To find the length of the perpendicular from the centre on the tangent. The length of the perpendicular from the origin on the line xx yy _ ~tf + ~„ = ' is (Art. 27) 1 ab... | |
 | Dublin city, univ - 1868 - 360 pages
...co-ordinates x'y' of any point on an ellipse being given by the equations z' = «cos0, y" = bsin<p, find the length of the perpendicular from the centre on the tangent at the point tfy in terms of 0. 6. Being given that lex — uvw find the value of a; 8 + y 2 7. Transform... | |
 | Philip Kelland - 1873 - 248 pages
...Ta.TßsinPCD=ab, or aW parallelograms circumscribing an ellipse are equal. 50. EXAMPLES. Ex. 1. To find the length of the perpendicular from the centre on the tangent. Let CY the perpendicular, which (Art. 45. Cor. 1) is a vector along фр, be хфр ; then since Y... | |
 | Philip Kelland, Peter Guthrie Tait - Quaternions - 1873 - 254 pages
...Tft sin PCD = ab, or all parallelograms circumscribing an ellipse are equal. 50. EXAMPLES. Ex. 1. To find the length of the perpendicular from the centre on the tangent. Let CY the perpendicular, which (Art. 45. Cor. 1) is a vector along <j>p, be x$p ; then since T is... | |
 | Sir George Greenhill - Mathematics - 1876 - 318 pages
...equatoreal and polar semicos~1 a 14-4] AND RIDERS. The electrification at any point is proportional to the length of the perpendicular from the centre on the tangent plane at the point, and if it be denoted by Xp, we must have f\pdS equal to the charge Q. But JpdS is three... | |
 | George Minchin Minchin - 1877 - 470 pages
...2 + A 2 > , , Differentiating this, regarding k and A as variables, we have by the well-known value of the perpendicular from the centre on the tangent plane of an ellipsoid. Substituting this value of dl; in (2), we have 4ny, a be x\ d\ ff-i = -- ; -- -. ' To find the limits... | |
 | George Minchin Minchin - Statics - 1880 - 536 pages
...O. If a tangent plane be drawn to this ellipsoid parallel to the plane whose stress is considered, the length of the perpendicular from the centre on the tangent plane represents the magnitude of the intensity of stress, as is obvious by squaring and adding the sides... | |
 | George Minchin Minchin - Statics - 1886 - 560 pages
...surface PQ, < Differentiating this, regarding & and A as variables, we have by the well-known value of the perpendicular from the centre on the tangent plane of an ellipsoid. * The curious compensation of errors involve.! in tlie usual proof of this U well noticed by Colliguon... | |
| |
... the length of the perpendicular from the centre on the tangent plane. 
