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Plane and solid analytic geometry (1921)

Osgood, William F. (William Fogg), 1864-1943, Graustein, William C. (William Caspar), 1888-1941, joint author · New York : The Macmillan Company · leaf 610

An illustration from Plane and solid analytic geometry, 1921, leaf 610
ated in a givenoctant intersect not only in Pbut also in one point of eachof the other octants; this isclear since all three surfacesare symmetric in each coordi-nate plane. Consequently, inthe so-called ellipsoidal coordi-nate system based on the con-focal quadrics there are eight points with the… … Fig. 5 (4) Ct^ + .r + z a^-\ b^-x • c^-x = 1, where X is arbitrary except that it shall not take on the valuesc2, 62^ a^. If A < c^, equation (4) defines the surfaces (1), etc.;finally, if A > a^, (4) has no locus. * Cf. Osgood, Differential and Integral Calculus, p. 326. 592 ANALYTIC…

Geometry, Analytic -- Plane · Geometry, Analytic -- Solid

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