 | Cambridge Philosophical Society - Science - 1883 - 360 pages
..._€S + €4 -€2+«4 l+3f + «3 112. In like manner for the passage from the 0-form to the .B-form, if X, Y, Z be the coordinates of a point on the spherical surface in regard to the ©-axes, Xt, Yt, Zt those of the same point iu regard to the .B-axes,... | |
 | George Salmon - Geometry, Analytic - 1862 - 490 pages
...dx ,dy ..dz ±d<& LddJL Ldd*_. oro * 0 * 0 ds d6 d ds ' do d ds ' de d ds> orp -ar> p ~dT' p ~dT ' If x', y', z be the co-ordinates of a point on the...the radius of curvature on the axes are x' — x, y — y, z' — z; but they are also p cos a, p cos/3, p cos7. Putting in then for cos a, cos/3, cos7... | |
 | Cambridge Philosophical Society - Philosophy - 1879 - 626 pages
...fall back upon the original investigation for the centro-surface. 85. In verification I remark that if X, Y, Z be the coordinates of a point on the curve of curvature in question, and (x, y, z) current coordinates, then the tangent plane of the torse, or... | |
 | Cambridge Philosophical Society - Science - 1879 - 616 pages
...fall back upon the original investigation for the centro-surface. 85. In verification I remark that if X, Y, Z be the coordinates of a point on the curve of curvature in question, and (x, y, z) current coordinates, then the tangent plane of the torse, or... | |
 | Cambridge Philosophical Society - Philosophy - 1883 - 332 pages
...+ e3 -t2 + t4 -t2 + t4 1+St + e3 112. In like manner for the passage from the 6-form to the 5-form, if X, Y, Z be the coordinates of a point on the spherical surface in regard to the 0-axes, Хг, Yt, Zt those of the same point in regard to the .ß-axes,... | |
 | Mathematics - 1890 - 146 pages
...that they may be perpendicular. Solution i^Prof. AIIINASII BASÛ, MA ; J. MACÜAHON, MA; and others. If (x, y, z) be the coordinates of a point on the resultant of (P, Q, R), then by taking moments Vx + Qy -t Rz = 0 (1), this is the equation in trilinears... | |
 | Arthur Cayley - Mathematics - 1891 - 646 pages
...curve. , Y, '»v Let be the equation of the given curve, (X, Y, Z) being current coordinates ; and let (x, y, z) be the coordinates of a point on the curve, so that we have Z7 = (•$*, y, *)" = 0, a condition satisfied by the coordinates of the point in question.... | |
 | Arthur Cayley - Mathematics - 1896 - 676 pages
...-e3 + f4 -£2+«* l + 3e + r' adcb 112. In like manner for the passage from the 0-form to the B-form, if X, Y, Z be the coordinates of a point on the spherical surface in regard to the ©-axes, Xt, Y3, Zt those of the same point in regard to the .B-axes,... | |
 | George Frederick Charles Searle - Elasticity - 1908 - 216 pages
...the new axis of y and cutting the plane OXZ in a straight line PQ inclined at an angle 6 to OX. Then, if x', y, z, be the coordinates of a point on the curve of intersection of the plane and the helicoid at a distance r from the new axis of y, we have x' =... | |
 | George Frederick Charles Searle - Elasticity - 1933 - 218 pages
...the new axis of y and cutting the plane OXZ in a straight line PQ inclined at an angle 6 to OX. Then, if x', y, z, be the coordinates of a point on the curve of inter^ection of the plane and the helicoid at a distance r from the new axis of y, we have x' =... | |
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Then, if x', y, z, be the coordinates of a point on the curve of intersection of the plane and the helicoid at a distance r from the new axis of y, we have x' = r cos 6, z = r sin 0, and thus, by (32), y = r(rcos0+p) r sin 0. 