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
... constant at a given point of a surface 288-291 . Remarks on the theorem of Art . 284 ib . 254 • ib . 256 257 292-295 . Conditions for the existence of umbilici 263 296 . 297 . Another investigation of the problem of Art . 280 Cauchy's ...
... constant at a given point of a surface 288-291 . Remarks on the theorem of Art . 284 ib . 254 • ib . 256 257 292-295 . Conditions for the existence of umbilici 263 296 . 297 . Another investigation of the problem of Art . 280 Cauchy's ...
Page 22
... constants in the equations ( 3 ) ; for , considering the left - hand equation , we see that it is the equation to a straight line in the plane of xz , which is evidently the projection of the given line on 22 THE STRAIGHT LINE .
... constants in the equations ( 3 ) ; for , considering the left - hand equation , we see that it is the equation to a straight line in the plane of xz , which is evidently the projection of the given line on 22 THE STRAIGHT LINE .
Page 23
... constants in its equations , and some of the more important cases we shall here consider . In the equations ( 2 ) , if a ... constant . If we consider the form ( 3 ) of the THE STRAIGHT LINE . 23 Two methods of applying analysis to Geometry.
... constants in its equations , and some of the more important cases we shall here consider . In the equations ( 2 ) , if a ... constant . If we consider the form ( 3 ) of the THE STRAIGHT LINE . 23 Two methods of applying analysis to Geometry.
Page 26
... constants in the equations to the lines , in order that they may intersect , and the condition must be also that which holds in order that the two lines may be in one plane . Let the equations to the lines be X- α у - в = m = 2 - n y ...
... constants in the equations to the lines , in order that they may intersect , and the condition must be also that which holds in order that the two lines may be in one plane . Let the equations to the lines be X- α у - в = m = 2 - n y ...
Page 29
... constant , while the values of x ' , y ' , z ' , vary in such a way as to satisfy the equations ( D ) : this we may denote by putting x ' , y ' , z ' , for x , y , z , in those equations . We then get x ' - lr , α = y ' - B = mr , xx ...
... constant , while the values of x ' , y ' , z ' , vary in such a way as to satisfy the equations ( D ) : this we may denote by putting x ' , y ' , z ' , for x , y , z , in those equations . We then get x ' - lr , α = y ' - B = mr , xx ...
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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...