A treatise on the application of analysis to solid geometry, commenced by D.F. Gregory, concluded by W. WaltonJ. Deighton, 1852 - 310 pages |
From inside the book
Results 1-5 of 33
Page xii
... Tangent lines and tangent planes 138 159. Property of the intersection of a surface with its tangent plane 141 160 . Skew surfaces and developable surfaces 142 ARTICLE 161-164 . Equations to the normal . Direction - xii CONTENTS .
... Tangent lines and tangent planes 138 159. Property of the intersection of a surface with its tangent plane 141 160 . Skew surfaces and developable surfaces 142 ARTICLE 161-164 . Equations to the normal . Direction - xii CONTENTS .
Page xiii
... Developable surfaces 199 239-240 . Developable surface circumscribing two given surfaces 202 241-243 . Tubular surfaces 205 244-245 . Example of an envelop having two independent parame- ters , Wave surface 207 CHAPTER XII . ARTICLE On ...
... Developable surfaces 199 239-240 . Developable surface circumscribing two given surfaces 202 241-243 . Tubular surfaces 205 244-245 . Example of an envelop having two independent parame- ters , Wave surface 207 CHAPTER XII . ARTICLE On ...
Page xiv
... Developable surfaces 216 217 254 . Tubular surfaces 218 255 . 256 . Symmetrical equation for developable surfaces Symmetrical equation for tubular surfaces 220 222 257 . Transformation from symmetrical to unsymmetrical forms 224 CHAPTER ...
... Developable surfaces 216 217 254 . Tubular surfaces 218 255 . 256 . Symmetrical equation for developable surfaces Symmetrical equation for tubular surfaces 220 222 257 . Transformation from symmetrical to unsymmetrical forms 224 CHAPTER ...
Page 121
... developable surfaces , of which the cone may be taken as the type . The reason of the term developable , and the nature of the distinction between these two classes of surfaces , will be explained in the chapter on Tangent Planes to ...
... developable surfaces , of which the cone may be taken as the type . The reason of the term developable , and the nature of the distinction between these two classes of surfaces , will be explained in the chapter on Tangent Planes to ...
Page 143
... account these surfaces are called developable surfaces : they will be more particularly treated of hereafter in the chapter on Envelops . 49 1 2 2 161. Definition . The normal to a surface at any TANGENTS OF SURFACES . 139.
... account these surfaces are called developable surfaces : they will be more particularly treated of hereafter in the chapter on Envelops . 49 1 2 2 161. Definition . The normal to a surface at any TANGENTS OF SURFACES . 139.
Other editions - View all
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...