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 x
... drawn from a given point on a plane , the equation to which is given ib . 49 . To find the length of the perpendicular from a given point on a given straight line 39 39 50 . To find the perpendicular distance between two straight lines ...
... drawn from a given point on a plane , the equation to which is given ib . 49 . To find the length of the perpendicular from a given point on a given straight line 39 39 50 . To find the perpendicular distance between two straight lines ...
Page xiii
... drawn after a given law ; characteristic and edge 193 234 . Envelops to surfaces which have several independent pa- rameters 198 • 235–238 . Developable surfaces 199 239-240 . Developable surface circumscribing two given surfaces 202 ...
... drawn after a given law ; characteristic and edge 193 234 . Envelops to surfaces which have several independent pa- rameters 198 • 235–238 . Developable surfaces 199 239-240 . Developable surface circumscribing two given surfaces 202 ...
Page 2
... draw PA , PB , PC , parallel to the three coordinate axes Ox , Oy , Oz , respectively , and meeting the coordinate planes in A , B , C ; then the position of the point P is known if we know the lengths of the lines PA , PB , and PC ...
... draw PA , PB , PC , parallel to the three coordinate axes Ox , Oy , Oz , respectively , and meeting the coordinate planes in A , B , C ; then the position of the point P is known if we know the lengths of the lines PA , PB , and PC ...
Page 3
... drawn through D , E , and F , with each other and with the coordinate planes , determine a parallelepiped , of which ... draw DC parallel to Oy and equal to PB , and through C draw CP parallel to Oz , making it of the given length , the ...
... drawn through D , E , and F , with each other and with the coordinate planes , determine a parallelepiped , of which ... draw DC parallel to Oy and equal to PB , and through C draw CP parallel to Oz , making it of the given length , the ...
Page 5
... draw a line parallel to the axis of z , and measure along it a length equal to the value of z given by the equation , it ... drawn through every point in the plane of xy . We here suppose that the equation 2 = = ( x , y ) gives only one ...
... draw a line parallel to the axis of z , and measure along it a length equal to the value of z given by the equation , it ... drawn through every point in the plane of xy . We here suppose that the equation 2 = = ( x , y ) gives only one ...
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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...