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 59
... homogeneous function of the second degree , u , of the first degree , and u , a constant . Let A ' = ( gh ) * , A = ƒ + λ , B ' = ( hƒ ) * , C ' = ( fg ) * , ... ( 3 ) , · B = g + μ2 C = h + v , B'C ' C'A ' 9 = B from which we ( 59 ) ...
... homogeneous function of the second degree , u , of the first degree , and u , a constant . Let A ' = ( gh ) * , A = ƒ + λ , B ' = ( hƒ ) * , C ' = ( fg ) * , ... ( 3 ) , · B = g + μ2 C = h + v , B'C ' C'A ' 9 = B from which we ( 59 ) ...
Page 69
... homogeneous function of the second degree , when equated to zero , represents in general a cone , the vertex of which is in the origin , unless 1st , The coefficients of the transformed equation are all of the same sign , when it ...
... homogeneous function of the second degree , when equated to zero , represents in general a cone , the vertex of which is in the origin , unless 1st , The coefficients of the transformed equation are all of the same sign , when it ...
Page 145
... homogeneous function of n dimensions , the equa- tion to the tangent plane is much simplified . For , by a well- known property of such functions , du X + y dx du du +2 = nu = nc ; dy dz so that the equation to the tangent plane becomes ...
... homogeneous function of n dimensions , the equa- tion to the tangent plane is much simplified . For , by a well- known property of such functions , du X + y dx du du +2 = nu = nc ; dy dz so that the equation to the tangent plane becomes ...
Page 146
... function of x , y , z , represents a surface which , by its intersection ... homogeneous functions of the degree indicated by the suffixes . becomes + + ... homogeneous functions , х dun n dx du n du en + z dz + y dy & c . = nun n du n ...
... function of x , y , z , represents a surface which , by its intersection ... homogeneous functions of the degree indicated by the suffixes . becomes + + ... homogeneous functions , х dun n dx du n du en + z dz + y dy & c . = nun n du n ...
Page 175
... homogeneous function of x , y , z , equated to zero : so that we have thus extended to all conical surfaces the remark made in Art . ( 79 ) on cones of the second degree . 204. Let the cone be that of which the director CONICAL SURFACES ...
... homogeneous function of x , y , z , equated to zero : so that we have thus extended to all conical surfaces the remark made in Art . ( 79 ) on cones of the second degree . 204. Let the cone be that of which the director CONICAL SURFACES ...
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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...