Examples of Analytical Geometry of Three Dimensions |
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Page 9
... 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 section always contains a given right line . Shew also that if the point of contact be not ...
... 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 section always contains a given right line . Shew also that if the point of contact be not ...
Page 10
... 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 axis of the cy ...
... 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 axis of the cy ...
Page 11
... sphere can be described through the 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 ...
... sphere can be described through the 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 ...
Page 12
... sphere of given radius whose centre moves in one of its prin- cipal planes ; find the locus of the centre of the sphere , and shew that it will describe a portion of an equilateral hyperbola , if the plane in which it moves be that ...
... sphere of given radius whose centre moves in one of its prin- cipal planes ; find the locus of the centre of the sphere , and shew that it will describe a portion of an equilateral hyperbola , if the plane in which it moves be that ...
Page 13
Isaac Todhunter. 86. If a sphere be placed in a paraboloid of revolution , shew that the section of the paraboloid made by any plane drawn touching the sphere is a conic section having the point of contact for a focus . 87. Shew that any ...
Isaac Todhunter. 86. If a sphere be placed in a paraboloid of revolution , shew that the section of the paraboloid made by any plane drawn touching the sphere is a conic section having the point of contact for a focus . 87. Shew that any ...
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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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