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
... taken as the plane of xy and the axis of z parallel to its chords 103-105 . Conjugate diametral planes 00 90 ib . 106 . To find the relations between oblique conjugate diameters and principal diameters of centric surfaces 107 . Remarks ...
... taken as the plane of xy and the axis of z parallel to its chords 103-105 . Conjugate diametral planes 00 90 ib . 106 . To find the relations between oblique conjugate diameters and principal diameters of centric surfaces 107 . Remarks ...
Page 5
... difference is that in each coordinate parallel to z we must take a determinate number of points , and these taken together will constitute a surface of several sheets . + - It is to be remarked , that though INTERPRETATION OF EQUATIONS . 5.
... difference is that in each coordinate parallel to z we must take a determinate number of points , and these taken together will constitute a surface of several sheets . + - It is to be remarked , that though INTERPRETATION OF EQUATIONS . 5.
Page 8
... taken together determine the curve of intersection , or , as it is called , the trace of the surface on the plane of xy . Even though the equation do not contain z , it must be combined with the equation 2 = 0 ; since , when taken by ...
... taken together determine the curve of intersection , or , as it is called , the trace of the surface on the plane of xy . Even though the equation do not contain z , it must be combined with the equation 2 = 0 ; since , when taken by ...
Page 20
... taken as proportional to the direction - cosines of some one line , and x , y , z , of another , the expression ax + by + cz ( a2 + b2 + c2 ) * ( x2 + y2 + z2 ) * is equal to the cosine of the angle between the lines : let this be ...
... taken as proportional to the direction - cosines of some one line , and x , y , z , of another , the expression ax + by + cz ( a2 + b2 + c2 ) * ( x2 + y2 + z2 ) * is equal to the cosine of the angle between the lines : let this be ...
Page 25
... taken in each case , there are only two sets of values for the cosines , corresponding to the supplementary values of the angles λ , μ , v , made with the positive axes of x , y , z , by the two portions of the line measured in opposite ...
... taken in each case , there are only two sets of values for the cosines , corresponding to the supplementary values of the angles λ , μ , v , made with the positive axes of x , y , z , by the two portions of the line measured in opposite ...
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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...