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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 590

An illustration from Plane and solid analytic geometry, 1921, leaf 590
iary variables, here they are given constants,and hence (4) is the equation satisfied by the point P of thelocus. But (4) represents a plane through the center of theellipsoid. Such a plane is known as a diametral plane. Thusour result is: Theorem 2. The locus of the mid-points of a set ofparallel… … QUADRIC SURFACES 571 Conjugate Dia^neters and Diametral Planes. Theorem 3. If a diameter D contains the centers of sectionsparallel to a diametral plane M, then M bisects the chordsparallel to D, and conversely. For, let D have the direction com-ponents I, m, n, and let M be the plane Ax-\-By+Cz =…

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

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