Examples of Analytical Geometry of Three Dimensions |
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Page 8
... ellipsoid such that the tangent plane cuts off equal intercepts from the axes . Also find a point such that the intercepts are proportional to the axes . 53. If a , b , c be the semiaxes of an ellipsoid taken in order , and e , e ' the ...
... ellipsoid such that the tangent plane cuts off equal intercepts from the axes . Also find a point such that the intercepts are proportional to the axes . 53. If a , b , c be the semiaxes of an ellipsoid taken in order , and e , e ' the ...
Page 9
... ellipsoid can be obtained by cutting it by planes passing through its mean axis . 61. A sphere ( C ) and a plane are given ; shew that if any sphere ( C ) be described touching the plane at a given point and cutting C , the plane of ...
... ellipsoid can be obtained by cutting it by planes passing through its mean axis . 61. A sphere ( C ) and a plane are given ; shew that if any sphere ( C ) be described touching the plane at a given point and cutting C , the plane of ...
Page 10
... ellipsoid , through the normal at that point , and through the centre of the ellipsoid . 67. A line passing through a given point moves so that the projection of any portion of it on a given line bears a con- stant ratio to the length ...
... ellipsoid , through the normal at that point , and through the centre of the ellipsoid . 67. A line passing through a given point moves so that the projection of any portion of it on a given line bears a con- stant ratio to the length ...
Page 11
... ellipsoid includes between itself and the co - ordinate planes a constant volume ; find the locus of the points of contact . 76. A tangent plane to an ellipsoid passes through a fixed point in one of the axes produced ; find the point ...
... ellipsoid includes between itself and the co - ordinate planes a constant volume ; find the locus of the points of contact . 76. A tangent plane to an ellipsoid passes through a fixed point in one of the axes produced ; find the point ...
Page 12
... ellipsoid at points in the curve of section pass through two straight lines situated in the other principal planes . 83. An ellipsoid is constantly touched in two points by a sphere of given radius whose centre moves in one of its prin ...
... ellipsoid at points in the curve of section pass through two straight lines situated in the other principal planes . 83. An ellipsoid is constantly touched in two points by a sphere of given radius whose centre moves in one of its prin ...
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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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