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 xv
... obtain an expression for the radius of curvature free from second differentials 246 277 . Remark on the double sign in the expression for the radius of curvature ib . 278 . Unsymmetrical form of the expression for the radius of ...
... obtain an expression for the radius of curvature free from second differentials 246 277 . Remark on the double sign in the expression for the radius of curvature ib . 278 . Unsymmetrical form of the expression for the radius of ...
Page 3
... obtain the point P by a simpler construction ; for , since OD = PA , DC = OE = PB , if along Оx we measure OD PA , and at D draw DC parallel to Oy and equal to PB , and through C draw CP parallel to Oz , making it of the given length ...
... obtain the point P by a simpler construction ; for , since OD = PA , DC = OE = PB , if along Оx we measure OD PA , and at D draw DC parallel to Oy and equal to PB , and through C draw CP parallel to Oz , making it of the given length ...
Page 5
... obtain from the equation a definite value for z . Now to every pair of values of x and y there corresponds a point in the plane of xy ; and if through this we draw a line parallel to the axis of z , and measure along it a length equal ...
... obtain from the equation a definite value for z . Now to every pair of values of x and y there corresponds a point in the plane of xy ; and if through this we draw a line parallel to the axis of z , and measure along it a length equal ...
Page 8
... obtain similar equations for each of the other axes , it appears that any line in space may be considered as the intersection of two cylindrical surfaces parallel to two of the coordinate axes . 10. If we wish to determine the curve in ...
... obtain similar equations for each of the other axes , it appears that any line in space may be considered as the intersection of two cylindrical surfaces parallel to two of the coordinate axes . 10. If we wish to determine the curve in ...
Page 20
... obtain as the result of any process that a function of x is equal to a function of y in which y is involved in a manner similar to that in which x is involved in the other , then , as there is nothing to distinguish one coordinate from ...
... obtain as the result of any process that a function of x is equal to a function of y in which y is involved in a manner similar to that in which x is involved in the other , then , as there is nothing to distinguish one coordinate from ...
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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...