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 172
r of the other. As Xassumes in turn all real values the line given by theequations (1) moves so as to completely generate the hyper-boloid. Similarly, the line given by the equations (2)moves, as fx varies, so as to generate the hyperboloid. Thehyperboloid of one sheet is therefore a ruled surface… … Fig. 41. Whence it is evident that the paraboloid is the locu^ >>tcither of the variable lines given by x y_z x y m a o X a h a 0 jul a b ^The hyperbolic paraboloid is therefore a ruled surface 150 COORDINATE GEOMETRY [ch. ix. and can be generated in two ways by the motion of astraight line.…
Geometry, Analytic
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