Examples of Analytical Geometry of Three Dimensions |
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Page 13
... conic section having the point of contact for a focus . 87. Shew that any plane parallel to the planes ... surface will the plane touch the surface in every point of the line ? 88. Through any point of the curve of intersection of the ...
... conic section having the point of contact for a focus . 87. Shew that any plane parallel to the planes ... surface will the plane touch the surface in every point of the line ? 88. Through any point of the curve of intersection of the ...
Page 26
... conical surface S so formed will inter- sect the ellipsoid in two planes parallel to the plane of contact . The locus of the vertex of the enveloping cone which causes one of the planes to coincide with the plane of contact is x2 , y2 ...
... conical surface S so formed will inter- sect the ellipsoid in two planes parallel to the plane of contact . The locus of the vertex of the enveloping cone which causes one of the planes to coincide with the plane of contact is x2 , y2 ...
Page 34
... conical surface is a " 112 a b " 2 + + b C'2 + ƒ = 0 . с 210. Shew that in order that the equation . ax2 + by2 + cz2 + 2a'yz + 2b'zx + 2c'xy + 2a ′′ x + 2b ′′ y + 2c " z + f = 0 may represent a cylindrical surface , it is necessary that ...
... conical surface is a " 112 a b " 2 + + b C'2 + ƒ = 0 . с 210. Shew that in order that the equation . ax2 + by2 + cz2 + 2a'yz + 2b'zx + 2c'xy + 2a ′′ x + 2b ′′ y + 2c " z + f = 0 may represent a cylindrical surface , it is necessary that ...
Page 40
... conic section . 248. A point moves on the cone y2 + z2 = m2x2 so that the ... surface of a right cone so as to cut the generating lines at a constant ... surface cutting all the generating lines at con- stant angles which are ...
... conic section . 248. A point moves on the cone y2 + z2 = m2x2 so that the ... surface of a right cone so as to cut the generating lines at a constant ... surface cutting all the generating lines at con- stant angles which are ...
Page 50
... conical surface ; and shew that the equa- tion to the tangent plane is Xu - 2λw + v = 0 . 308. Let v = 0 be the equation to a surface of the second order ; u = 0 and u , = 0 the equations to two planes ; shew that by giving a suitable ...
... conical surface ; and shew that the equa- tion to the tangent plane is Xu - 2λw + v = 0 . 308. Let v = 0 be the equation to a surface of the second order ; u = 0 and u , = 0 the equations to two planes ; shew that by giving a suitable ...
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Common terms and phrases
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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Page 15 - PROCTER— A HISTORY OF THE BOOK OF COMMON PRAYER, with a Rationale of its Offices. By FRANCIS PROCTER, MA Thirteenth Edition, revised and enlarged. Crown 8vo. loг. 6d. PROCTER AND MACLEAR— AN ELEMENTARY INTRODUCTION TO THE BOOK OF COMMON PRAYER.
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