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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... origin of coordinates , the axes remaining parallel to their original position 49 60 . To pass from a rectangular system to any other , the origin remaining the same 50 • 61-64 . To pass from one system of rectangular coordinates to ...
... origin of coordinates , the axes remaining parallel to their original position 49 60 . To pass from a rectangular system to any other , the origin remaining the same 50 • 61-64 . To pass from one system of rectangular coordinates to ...
Page 2
... origin . Each of these lines may be considered as determined by the intersection two and two of three planes . Thus , in fig . ( 1 ) , if Ox , Oy , Oz , be the three coordinate axes , O the origin , we may consider the axis Ox as the ...
... origin . Each of these lines may be considered as determined by the intersection two and two of three planes . Thus , in fig . ( 1 ) , if Ox , Oy , Oz , be the three coordinate axes , O the origin , we may consider the axis Ox as the ...
Page 9
... origin . 13. The general property of all orthogonal projections of bounded straight lines or plane areas , is that the projections are equal to the original line or area multiplied by the cosine of the angle between the straight line or ...
... origin . 13. The general property of all orthogonal projections of bounded straight lines or plane areas , is that the projections are equal to the original line or area multiplied by the cosine of the angle between the straight line or ...
Page 13
... origin , then x1 = 0 , y1 = 0 , z1 = 0 , and we have for the distance of P from the origin , OP = ( x2 + y2 + z2 ) * . 15. To express the distance between two points in terms of their oblique coordinates . Make a construction similar to ...
... origin , then x1 = 0 , y1 = 0 , z1 = 0 , and we have for the distance of P from the origin , OP = ( x2 + y2 + z2 ) * . 15. To express the distance between two points in terms of their oblique coordinates . Make a construction similar to ...
Page 14
... origin 0 ( fig . 8 ) in the line , let POx POy = B , POz = y , and let x , y , z , be the coordinates of any point P in the line ; then , if the distance OP be r , we have , by Art . ( 14 ) , p2 = x2 + y2 + 2 * : but , since x , y , z ...
... origin 0 ( fig . 8 ) in the line , let POx POy = B , POz = y , and let x , y , z , be the coordinates of any point P in the line ; then , if the distance OP be r , we have , by Art . ( 14 ) , p2 = x2 + y2 + 2 * : but , since x , y , z ...
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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...