A treatise on solid geometry, by P. Frost and J. Wolstenholme1863 |
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Common terms and phrases
asymptotic ax² axes axis by² circular sections cone conicoid constant corresponding cos² cosines curve of intersection cylinder determined developable surface directing planes direction-cosines directrix drawn dx dy ellipse ellipsoid envelope equal find the equation fixed plane fixed point focal conic focal curve geodesic given plane given point given straight line Hence hyperbolic paraboloid hyperboloid infinite distance infinite number Let the equation line joining line of curvature line of intersection locus normal nth degree obtain osculating plane P₁ parabola perpendicular plane containing plane curve plane of xy plane passing plane section plane whose equation points of intersection polar plane pole principal planes projection radius ratio reciprocal right angles satisfy the equation second degree shew sin² sphere tangent plane tetrahedron values vertex x² y²
Popular passages
Page 472 - THE FIRST THREE SECTIONS OF NEWTON'S PRINCIPIA, With Notes and Illustrations. Also a collection of Problems, principally intended as Examples of Newton's Methods. By PERCIVAL FROST, MA Third Edition.
Page 475 - Mr. Smith's Work is a most useful publication. The Rules are stated with great clearness. The P^xamples are well selected and worked out with just sufficient detail without being encumbered by too minute explanations ; and there prevails throughout it that just proportion of theory and practice, which is the crowning excellence of an elementary work.
Page 98 - The hyperboloid of one sheet may be generated by the motion of a variable ellipse, which moves so that its plane is always parallel to a fixed plane, and which changes its form so that its vertices always lie in two hyperbolas traced on planes perpendicular to each other and to the fixed plane, these hyperbolas having a common conjugate axis.
Page 135 - Conic, is the locus of a point which moves so that its distance from a fixed point is in a constant ratio to its distance from a fixed straight line.