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 187
eform, (1) y = b, z = — c; (2) z = c, x— — a; (3) x = a, y = — b,where 2a, 26, 2c are the edges. The general equation to aconicoid through the lines (1) and (2) is(y-b)(z-c) + \(y-b)(x+a) +iu(z+c)(z-c)+v(z+c)(x+a) = 0.Where x = a, y= —b meets the surface we have/ulz2+2z(av-b)- //c2 + 2c (av + b) -… … Fig. 46. The origin evidently bisects all chords of the surfacewhich pass through it, and therefore the surface is acentral surface, and is therefore a hyperboloid of one sheet.(Cf. §47, Ex. 1.) If the three lines are parallel to the same plane, let anyline which meets them be taken as 2-axis. If…
Geometry, Analytic
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