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Caption: Mathematical Models Catalog of a Collection of Models of Ruled Surfaces
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28 therefore , dz dz dx dy which is the differential equation of all cylindrical surfaces whose director ratios are I, mP n. If w e take the functional equation f _ i = f (y. \m n m \m w e obtain by partial differentiation dz dx i / n -wV dz __ % _ u _,, I D dy m m 1 dz dz . , , , . • o ~.—\~ m ~r == n && before. . ax dy Conical Surfaces. O u r object here is to retain a,fi,y, and to get rid of l9 m,ft,by differentiation. For this purpose write y~.fi ?i m y ~~ $ ~m ~ x — o o I <y-0(1 +flD~ <*-*>* = °(.,_a)|„(y_/3) = 0„ / 0, ( dz 1/ — fi dz ) y - fi w ' (ax x •— a a y ) or , dz , : _N dz is the differential equation of the surface. Conoids. ' T h e generating line is, for the simplest form, y s^ kx, z = ce t dz ^ d z cly^ Q dy _ ^ _ y ° dx dy dx 3 dx x eliminating -—, the partial differential equation of the surface is dz dx dz dy x — <> *
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