Woods, Frederick S. (Frederick Shenstone), 1864-, Bailey, Frederick H. (Frederick Harold), 1865- · Boston, New York [etc.] Ginn and Company · leaf 327
is. c2 >rPlacing z = 0, we have — — 2-=l, an hyperbola, as the generatinga- b- curve. The hyperbola was revolved about its conjugate axis. Conversely, if we have any plane curve F(x, z) = 0 in theplane XOZ, the equation of the surface formed by revolving itabout OZ as an axis is F(Vx2 + y2, z) =… … Replacing a by Vy2 + z2, we have as the equation of the sphere, x2 + y- + z2 = a2. This equation may also befound directly from a figure. Let Px (fig. 195) be any pointof the circle, and .let P be anypoint of the sphere, on the circledescribed by Pv Since Px is apoint of the circle, OZ2 + TP{ = a2.…
Geometry, Analytic · Calculus
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