A treatise on solid geometry, by P. Frost and J. Wolstenholme1863 |
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Page xii
... Circular sections of oblique circular cone Equation of a spheroid Equation of an ellipsoid Construction of the locus of the equation Equation of an hyperboloid of one sheet ..... Construction of the locus of the equation Asymptotic ...
... Circular sections of oblique circular cone Equation of a spheroid Equation of an ellipsoid Construction of the locus of the equation Equation of an hyperboloid of one sheet ..... Construction of the locus of the equation Asymptotic ...
Page xiii
... section of a central surface , when circular ; locus of centers of circular sections 125 Two circular sections of opposite systems lie in one sphere 128 Circular sections of non - central surfaces .... Circular sections of an elliptic ...
... section of a central surface , when circular ; locus of centers of circular sections 125 Two circular sections of opposite systems lie in one sphere 128 Circular sections of non - central surfaces .... Circular sections of an elliptic ...
Page xx
... circular sec- tions of an ellipsoid Locus of ultimate intersection of surfaces , the general equation of which in- volves two arbitrary parameters 363 364 " " area ..... Envelope of diametral planes of an ellipsoid whose sections are of ...
... circular sec- tions of an ellipsoid Locus of ultimate intersection of surfaces , the general equation of which in- volves two arbitrary parameters 363 364 " " area ..... Envelope of diametral planes of an ellipsoid whose sections are of ...
Page xxii
... section 416 Sections and radii of principal curvature Conditions for an umbilicus Line of spherical curvature Number ... circular cylinder Geodesic on right cone 449 450 Number of geodesics on cone Geodesic on surface of revolution pd ...
... section 416 Sections and radii of principal curvature Conditions for an umbilicus Line of spherical curvature Number ... circular cylinder Geodesic on right cone 449 450 Number of geodesics on cone Geodesic on surface of revolution pd ...
Page xxiii
... circular section ..... Intersection of a geodesic through an umbilicus with a geodesic tangent to a line of curvature which it meets at a constant angle lies on one of two spheres Tangent lines to a geodesic on a conicoid touch a fixed ...
... circular section ..... Intersection of a geodesic through an umbilicus with a geodesic tangent to a line of curvature which it meets at a constant angle lies on one of two spheres Tangent lines to a geodesic on a conicoid touch a fixed ...
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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.