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 33
f(z, x) = 0 represent cylinders generated byparallels to OX and OY respectively. Ex. What surfaces are represented by (i) x2+y2 = a2, (ii) y2 = 4ax,the axes being rectangular ? Two equations are necessary to determine the curve inthe plane XOY. The curve is on the cylinder whose equa-tion is f(x,… … (The surface shewn is represented by the equationa2xi + biyi—zi.) Consider now the equation fix, y, z) = 0. The equationz = k represents a plane parallel to XOY, and the equationf(x, y, Z?) = 0 represents, as we have just proved, a cylinder §9] THE EQUATION TO A 81 ll \< I. n generated by lines…
Geometry, Analytic
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