An elementary treatise on coordinate geometry of three dimensions (1912)
Bell, Robert J. T. (Robert John Tainsh), 1877-1963 · London : Macmillan and co., limited · leaf 319
to the axis. From fig. 58 we obtain Whence dr=dR sin oc = dz tan a, ^dR = ds cos B = r dd cot B. J — = cot 8 sin a. dO, (1) which is the differential equation to the projection and has as integral fcs where k = cot B sin a. and A is arbitrary. 296 COOKDINATE GEOMETEY [CH. XIV. dzAgain, from (1),… … Fig. 58. Now %=rco&$, y=rsind, and, using dashes to denote differentiation with respect to s, by (1), /=sin a. cos /?, and rd = sin (3.Therefore x=r cos 6 — sin (3 sin 9, y = r sin 6 + sin /3 cos 6 ; a; = - (/ sin 6 + sin /3 cos #) 6, y = (/ cos 0 - sin /3 sin 0) #; 1 = ^(/Hsin^) = sin^(1 ~…
Geometry, Analytic
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