Examples of Analytical Geometry of Three DimensionsMacmillan, 1864 - 84 páginas |
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Página 9
... contact be not given , and if the plane of section always contain a given point , the centre of the sphere C ' will ... points of con- tact of the tangent planes with the ellipsoid . 64. If tangent planes be drawn to an ellipsoid from any ...
... contact be not given , and if the plane of section always contain a given point , the centre of the sphere C ' will ... points of con- tact of the tangent planes with the ellipsoid . 64. If tangent planes be drawn to an ellipsoid from any ...
Página 11
... contact provided P be on a certain right line passing through the origin . 73. A sphere touches each of two right ... points of contact . 76. A tangent plane to an ellipsoid passes through a fixed point in one of the axes produced ; find ...
... contact provided P be on a certain right line passing through the origin . 73. A sphere touches each of two right ... points of contact . 76. A tangent plane to an ellipsoid passes through a fixed point in one of the axes produced ; find ...
Página 13
... point of contact for a focus . 87. Shew that any plane parallel to the planes of ( x , z ) or ( y , z ) will meet the surface whose equation is xy = az in a straight line ; if a plane be made to pass through that line and touch the ...
... point of contact for a focus . 87. Shew that any plane parallel to the planes of ( x , z ) or ( y , z ) will meet the surface whose equation is xy = az in a straight line ; if a plane be made to pass through that line and touch the ...
Página 16
... point , the points of contact , and the centre of the given ellipsoid . 107. Normals are drawn to the ellipsoid x2 , y2 ++ = 1 at the points where it is intersected by the plane zh . Shew that the locus of the intersection of these ...
... point , the points of contact , and the centre of the given ellipsoid . 107. Normals are drawn to the ellipsoid x2 , y2 ++ = 1 at the points where it is intersected by the plane zh . Shew that the locus of the intersection of these ...
Página 24
... point P such that if PQ be drawn perpendicular to EF to meet LM in Q , then PQ may bear an ... contact of a second tangent plane to the ellipsoid , P will be the ... points Q1 , Q2 , Q. , respectively , 1 1 + 2 1 + 1 1 1 = + + · 2 167. A ...
... point P such that if PQ be drawn perpendicular to EF to meet LM in Q , then PQ may bear an ... contact of a second tangent plane to the ellipsoid , P will be the ... points Q1 , Q2 , Q. , respectively , 1 1 + 2 1 + 1 1 1 = + + · 2 167. A ...
Otras ediciones - Ver todo
Examples of Analytical Geometry of Three Dimensions Isaac Todhunter No hay ninguna vista previa disponible - 2019 |
Examples of Analytical Geometry of Three Dimensions Isaac Todhunter No hay ninguna vista previa disponible - 2018 |
Términos y frases comunes
Algebra Arithmetic ax² axis by² Calculus centre circle cloth co-ordinate planes Collection of Examples Conic Sections conical surface conjugate diameters constant contains cos² Crown 8vo curve of intersection cylinder determined developable surface differential equation distance ELEMENTARY ellipse ellipsoid English Find the equation find the locus fixed point fixed straight lines given plane given point hyperbolic hyperboloid John's College late Fellow Latin line of intersection Morocco numerous Examples origin osculating plane parabola paraboloid plane parallel plane passing plane which passes planes are drawn points of contact principal radii principal sections radii of curvature represent right angles right cone Second Edition second order shew sphere ST JOHN'S COLLEGE student surface of revolution surface whose equation tangent plane tetrahedron tions Treatise vertex volume x² y² y² z² y²+z²
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