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 vii
... Second Order , ” and “ On the Lines of Curvature of Surfaces of the Second Order , " have been incorporated in this work in place of the investiga- tions which appeared in the former edition . In the Appendix , I have given , together ...
... Second Order , ” and “ On the Lines of Curvature of Surfaces of the Second Order , " have been incorporated in this work in place of the investiga- tions which appeared in the former edition . In the Appendix , I have given , together ...
Page xvi
... second order 276 303 . Dupin's Theorem 282 PROBLEMS APPENDIX CHAPTER XVI . ERRATA . Page Line 25 , 17 , 62 , 7 from bottom , Error . Equation . " 2 " , 71 , 5 from bottom , P > Q , Q , 88 , 5 , c ′ ) , 97 , 8 , 139 , Correction ...
... second order 276 303 . Dupin's Theorem 282 PROBLEMS APPENDIX CHAPTER XVI . ERRATA . Page Line 25 , 17 , 62 , 7 from bottom , Error . Equation . " 2 " , 71 , 5 from bottom , P > Q , Q , 88 , 5 , c ′ ) , 97 , 8 , 139 , Correction ...
Page 21
... second order will be treated by the other method . In the following investigations the coordinates are considered as rectangular , except when the contrary is expressly stated . The Straight Line . 24. To find the equations to a ...
... second order will be treated by the other method . In the following investigations the coordinates are considered as rectangular , except when the contrary is expressly stated . The Straight Line . 24. To find the equations to a ...
Page 26
... second , member by member , we have = X- x1 y - y1 2-2 x - x1 Դ 1 = 22-21 as the required equations . 30. To find ... order that they may intersect , and the condition must be also that which holds in order that the two lines may be in ...
... second , member by member , we have = X- x1 y - y1 2-2 x - x1 Դ 1 = 22-21 as the required equations . 30. To find ... order that they may intersect , and the condition must be also that which holds in order that the two lines may be in ...
Page 55
... degree , and consequently the degree of the equation cannot be raised . Neither in the second place can it be lowered , TRANSFORMATION OF COORDINATES . 55 Degree of an equation not affected by transformation coordinates 68-69 ...
... degree , and consequently the degree of the equation cannot be raised . Neither in the second place can it be lowered , TRANSFORMATION OF COORDINATES . 55 Degree of an equation not affected by transformation coordinates 68-69 ...
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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...