. Plane and solid analytic geometry; an elementary textbook. Eig. 18. The section of the surface made by the X-F-plane is anhyperbola, with its transverse axis 2 a along the X-axis;the section made by the Z-X-plane is also an hyperbola,with its transverse axis 2 a along the X-axis; the sectionby the P-^-plane is imaginary. Sections made by planes parallel to the Y-Z-plane areimaginary for values of x between + a and — a. Whenx = ± a, the sections are null ellipses, and for values of xnumerically greater than a the sections are ellipses, in-creasing indefinitely as the cutting plane recedes fro
. Plane and solid analytic geometry; an elementary textbook. Eig. 18. The section of the surface made by the X-F-plane is anhyperbola, with its transverse axis 2 a along the X-axis;the section made by the Z-X-plane is also an hyperbola,with its transverse axis 2 a along the X-axis; the sectionby the P-^-plane is imaginary. Sections made by planes parallel to the Y-Z-plane areimaginary for values of x between + a and — a. Whenx = ± a, the sections are null ellipses, and for values of xnumerically greater than a the sections are ellipses, in-creasing indefinitely as the cutting plane recedes from theorigin. The sections of the surface made by planes parallel to Ch. V, § 30] QUADEIC SURFACES 239 the X-Y and Z-X planes are hyperbolas, and it may alsobe shown by the aid of transformation of coordinates thatall planes through the X-axis are hyperbolas. This surface is called the hyperboloid of two sheets, orthe biparted hyperboloid, extending along the X-axis. The.
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