Examples of Analytical Geometry of Three Dimensions |
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Page 5
... prove the following theorem ; a triangle is projected on each of three rectangular planes ; shew that the sum of the pyramids which have these projections for bases and a com- mon vertex in the plane of the triangle is equal to the ...
... prove the following theorem ; a triangle is projected on each of three rectangular planes ; shew that the sum of the pyramids which have these projections for bases and a com- mon vertex in the plane of the triangle is equal to the ...
Page 6
... prove that the number of lines of intersection of the planes is number of points of intersection of those lines is 41 . - n ( n − 1 ) ( n − 2 ) 1.2.3 n 2 - ( n − 1 ) , and that the Find the shortest distance between the point ( a , B ...
... prove that the number of lines of intersection of the planes is number of points of intersection of those lines is 41 . - n ( n − 1 ) ( n − 2 ) 1.2.3 n 2 - ( n − 1 ) , and that the Find the shortest distance between the point ( a , B ...
Page 9
... prove that 1 1 = + 63. Tangent planes are drawn to an ellipsoid from a given external point ; find the equation to the cone which has its vertex at the origin and passes through all the points of con- tact of the tangent planes with the ...
... prove that 1 1 = + 63. Tangent planes are drawn to an ellipsoid from a given external point ; find the equation to the cone which has its vertex at the origin and passes through all the points of con- tact of the tangent planes with the ...
Page 10
... Prove that the axis of the cy- linder is invariable in position , and that the area of its trans- verse section varies as the surface of the sphere . 71. Three edges of a tetrahedron , in length a , b , and c , are mutually at right ...
... Prove that the axis of the cy- linder is invariable in position , and that the area of its trans- verse section varies as the surface of the sphere . 71. Three edges of a tetrahedron , in length a , b , and c , are mutually at right ...
Page 11
... prove that a 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 ...
... prove that a 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 ...
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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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