A treatise on the application of analysis to solid geometry, commenced by D.F. Gregory, concluded by W. WaltonJ. Deighton, 1852 - 310 pages |
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Page xi
... surfaces of the second degree CHAPTER VI . Theorems relating to Surfaces of the Second Degree . 81 5788 67 77 80 95-99 . Diametral planes . 84 100-101 . Principal diametral planes 88 102. Form of the equation to the surface when a ...
... surfaces of the second degree CHAPTER VI . Theorems relating to Surfaces of the Second Degree . 81 5788 67 77 80 95-99 . Diametral planes . 84 100-101 . Principal diametral planes 88 102. Form of the equation to the surface when a ...
Page xii
... surface of the same sphere 129-132 . Conditions that the equation of the second degree shall represent surfaces of revolution 133-142 . Rectilinear generating lines 107 108 112 113 119 CHAPTER VII . On Curves in Space . 143-144 ...
... surface of the same sphere 129-132 . Conditions that the equation of the second degree shall represent surfaces of revolution 133-142 . Rectilinear generating lines 107 108 112 113 119 CHAPTER VII . On Curves in Space . 143-144 ...
Page xiii
... surfaces 178 212-216 . Skew surfaces having more than one director 183 217-220 . Developable surfaces 186 221-224 . Surfaces of revolution 189 CHAPTER XI . Envelops to Surfaces . 225-233 . Envelops ; equation to the surface which ...
... surfaces 178 212-216 . Skew surfaces having more than one director 183 217-220 . Developable surfaces 186 221-224 . Surfaces of revolution 189 CHAPTER XI . Envelops to Surfaces . 225-233 . Envelops ; equation to the surface which ...
Page xiv
... surfaces 212 249 . Conical surfaces 213 250 . Conoidal surfaces 214 251 . Surfaces of revolution 216 • 252 . 253 . Ruled surfaces having a director plane Developable surfaces 216 217 254 . Tubular surfaces 218 255 . 256 . Symmetrical ...
... surfaces 212 249 . Conical surfaces 213 250 . Conoidal surfaces 214 251 . Surfaces of revolution 216 • 252 . 253 . Ruled surfaces having a director plane Developable surfaces 216 217 254 . Tubular surfaces 218 255 . 256 . Symmetrical ...
Page xv
... surface in relation to the tangent plane To find the greatest and least radii of curvature of the normal sections at any point of a surface ib . 249 281 . 282 . 283 . 284 . 285 . To shew that the normal sections of greatest and least ...
... surface in relation to the tangent plane To find the greatest and least radii of curvature of the normal sections at any point of a surface ib . 249 281 . 282 . 283 . 284 . 285 . To shew that the normal sections of greatest and least ...
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Common terms and phrases
axis centre chords coefficients condition cone constant coordinate planes cosines cosn cosß cosv cosy curvature curve of contact cylinder determined developable surface dF dF dF dx diametral plane direction-cosines dv du dv dx dy dz dx² eliminating ellipse ellipsoid equa equal expression find the equation formulæ geometrical given line Hence homogeneous function hyperbolic hyperbolic paraboloid hyperboloid infinite number Let the equations line of intersection lines of curvature locus Multiplying normal plane origin osculating circle osculating plane parameters perpendicular plane curve plane of yz planes parallel positive projection Px² quantities Qy² ratios rectangular ruled surfaces Rz² second degree second order sections shew singular points sphere straight line substitute tangent plane three equations values vanish variables x₁ x²² Y₁ y²² zero
Popular passages
Page 16 - To express the area of a triangle in terms of the coordinates of its angular points.
Page 307 - A Treatise on the Application of Analysis to Solid Geometry. Commenced by DF GREGORY, MA, late Fellow and Assistant Tutor of Trinity College, Cambridge ; Concluded by W. WALTON, MA, Trinity College, Cambridge.
Page 10 - It, so that PR is equal to MN. Now the inclination of a straight line to a plane is the angle which the line makes with the intersection of the plane and a plane perpendicular to it passing through the line. Since, then, PM and QN are perpendicular to ABCD, the plane of PQMN is also perpendicular to it, and the inclination of PQ to the plane AB CD is measured by the angle between PQ and MN or the equal angle QPR.
Page 280 - The sum of the squares of the projections of any three conjugate diameters on a fixed line is constant. Instead of projecting the diameters on the line directly, it is better to project the coordinates of the extremities of each diameter, and add them. Now, if X...