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 4
... negative . Then , if lines measured from towards x ( fig . 2 ) be positive , those measured from O towards x ' are negative ; and if lines measured from O towards y be positive , those measured from 0 towards y ' are negative ; and if ...
... negative . Then , if lines measured from towards x ( fig . 2 ) be positive , those measured from O towards x ' are negative ; and if lines measured from O towards y be positive , those measured from 0 towards y ' are negative ; and if ...
Page 28
... negative , corresponding to the acute and the obtuse angles which the two lines make with each other . The expression for the sine will also have two equal values with opposite signs . In fact , suppose the angle AOB between two lines ...
... negative , corresponding to the acute and the obtuse angles which the two lines make with each other . The expression for the sine will also have two equal values with opposite signs . In fact , suppose the angle AOB between two lines ...
Page 39
... negative , we must then take the denomi- nator with the negative sign , since the value of 8 is absolute , and must therefore be considered as positive . 49. To find the length of the perpendicular from a given point on a given straight ...
... negative , we must then take the denomi- nator with the negative sign , since the value of 8 is absolute , and must therefore be considered as positive . 49. To find the length of the perpendicular from a given point on a given straight ...
Page 49
... new . But if E either chance to lie in the direction of any negative ( 49 ) CHAPTER III Transformation of Coordinates To change the origin of coordinates, the axes remaining parallel to their original position CHAPTER XVI.
... new . But if E either chance to lie in the direction of any negative ( 49 ) CHAPTER III Transformation of Coordinates To change the origin of coordinates, the axes remaining parallel to their original position CHAPTER XVI.
Page 50
... negative axis of y ' , and so forth . y = B− y ' ; Hence the formulæ ( 1 ) are true for all cases , if we attach to the quantities involved their proper signs depend- ing on their positions relative to the origins . These formula hold ...
... negative axis of y ' , and so forth . y = B− y ' ; Hence the formulæ ( 1 ) are true for all cases , if we attach to the quantities involved their proper signs depend- ing on their positions relative to the origins . These formula hold ...
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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...