Tanner, J. H. (John Henry), b. 1861, Allen, Joseph · New York, American Book Co · leaf 272
s are called, respectively, ellip-soids, hyperboloids, paraboloids, and cartes; and each species hasspecial varieties, depending upon the nature of a second sys-tem of plane sections. 155. The ellipsoid: equation ^-)-^-f^=l. From the a 6 c*equation «2 62 C2 * ■^■ the following properties of its… … Fia. 101. (2) The traces on planes parallel to any coordinate planeare similar ellipses [Art. 153]. (3) Tlie equation may be written 6(o-a^) + 0? = 1; hence for a plane section parallel to the ^z-plane, the semi-axes are real if the value of x lies between — a and -(- a,imaginary if beyond those…
Geometry, Analytic
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