Examples of Analytical Geometry of Three Dimensions |
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Page 9
... curve which contains all the points of contact will lie in a plane which always cuts the axis of z in the same point . 65. Shew that the tangent plane to an ellipsoid is ex- pressed by the equation lx + my + nz = √√ ( l3a2 + m2b2 + ...
... curve which contains all the points of contact will lie in a plane which always cuts the axis of z in the same point . 65. Shew that the tangent plane to an ellipsoid is ex- pressed by the equation lx + my + nz = √√ ( l3a2 + m2b2 + ...
Page 10
... curve by a variable sphere , and a variable cylinder ; the cylinder is always parallel to the least axis of the ellipsoid , and the centre of the sphere is always at the focus of a principal section containing this axis . Prove that the ...
... curve by a variable sphere , and a variable cylinder ; the cylinder is always parallel to the least axis of the ellipsoid , and the centre of the sphere is always at the focus of a principal section containing this axis . Prove that the ...
Page 11
... curve of contact provided P be on a certain right line passing through the origin . 73. A sphere touches each of two right lines which are inclined to each other at a right angle but do not meet ; shew that the locus of its centre is an ...
... curve of contact provided P be on a certain right line passing through the origin . 73. A sphere touches each of two right lines which are inclined to each other at a right angle but do not meet ; shew that the locus of its centre is an ...
Page 12
... curve in a plane perpendicular to that of ( b , c ) if the vertex of the cone be point of the surface 2 y2 x2 + 다 . b2 a2 = 1 . any 82. An ellipsoid is cut by a plane parallel to one of its principal planes ; shew that all normals to ...
... curve in a plane perpendicular to that of ( b , c ) if the vertex of the cone be point of the surface 2 y2 x2 + 다 . b2 a2 = 1 . any 82. An ellipsoid is cut by a plane parallel to one of its principal planes ; shew that all normals to ...
Page 13
... curve of intersection of the surfaces x2 , y2 z2 + - a2 + b2 c2 = · 1 , x2 + y2 + z2 = a2 + b2 — c3 , two straight lines can be drawn on the former surface at right angles to one another . 89. Prove that the plane z = mx + ny will cut ...
... curve of intersection of the surfaces x2 , y2 z2 + - a2 + b2 c2 = · 1 , x2 + y2 + z2 = a2 + b2 — c3 , two straight lines can be drawn on the former surface at right angles to one another . 89. Prove that the plane z = mx + ny will cut ...
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Common terms and phrases
a²x² ax² by² centre circle cloth co-ordinate planes CO.'S PUBLICATIONS conic section conical surface conjugate diameters constant Crown 8vo curve of intersection cylinder cz² developable surface distance ellipse ellipsoid equation x² Fcap Fellow of St Fellow of Trinity Find the equation find the locus fixed point fixed straight line given plane given point hyperbolic hyperboloid John's College late Fellow line of intersection M.A. Fellow MACMILLAN & CO.'S origin osculating plane parabola paraboloid plane parallel plane passing plane which passes planes are drawn planes of contact points of contact principal radii prove radii of curvature radius right angles Second Edition second order Sermons sewed shew sphere surface of revolution surface whose equation surface x² tangent plane Treatise Trinity College University of Cambridge vertex x² y² y² z² y²+z²
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