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 9
... meets the plane is called the projection of the point on the plane . Thus in fig . ( 1 ) A is the projection of P on the plane of yz , B is the projection on the plane of zx , and C that on xy . If a series of points , forming a line ...
... meets the plane is called the projection of the point on the plane . Thus in fig . ( 1 ) A is the projection of P on the plane of yz , B is the projection on the plane of zx , and C that on xy . If a series of points , forming a line ...
Page 10
... meet , their inclination is measured by the angle between one of them , and a parallel to the other drawn through any point in it . Draw PM , QN , perpendicular to AB ; then , by definition , MN is the projection of PQ on AB . Through ...
... meet , their inclination is measured by the angle between one of them , and a parallel to the other drawn through any point in it . Draw PM , QN , perpendicular to AB ; then , by definition , MN is the projection of PQ on AB . Through ...
Page 15
... meet , the angle between them is found by drawing through any point in the one a line parallel to the other . Take this point as the origin 0 ( fig . 9 ) ; let a , ß , y , be the angles which OP , and a ,, B1 , Y1 , those which OQ makes ...
... meet , the angle between them is found by drawing through any point in the one a line parallel to the other . Take this point as the origin 0 ( fig . 9 ) ; let a , ß , y , be the angles which OP , and a ,, B1 , Y1 , those which OQ makes ...
Page 26
... meet , the coordinates x , y , z , of the point of intersection must satisfy the equations to both lines . Hence , x , y , z , are the same in ( 1 ' ) and ( 2 ' ) ; therefore , subtracting each equation of ( 2 ' ) from the corresponding ...
... meet , the coordinates x , y , z , of the point of intersection must satisfy the equations to both lines . Hence , x , y , z , are the same in ( 1 ' ) and ( 2 ' ) ; therefore , subtracting each equation of ( 2 ' ) from the corresponding ...
Page 39
... meets ( 1 ) , the nume- rator of the former of these is the perpendicular distance of the point from the plane . Let this be 8 ; then , as ( x , y , z ) is a point in the plane , we have , by ( 1 ) , and consequently = Ax + By + Cz = D ...
... meets ( 1 ) , the nume- rator of the former of these is the perpendicular distance of the point from the plane . Let this be 8 ; then , as ( x , y , z ) is a point in the plane , we have , by ( 1 ) , and consequently = Ax + By + Cz = D ...
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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...