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 1
... fixed lines intersecting each other in one point . And the mode by which this is done is the characteristic feature of the Application of Analysis to Geometry . B Any fixed line is called an axis , and the CHAPTER I Exposition of ...
... fixed lines intersecting each other in one point . And the mode by which this is done is the characteristic feature of the Application of Analysis to Geometry . B Any fixed line is called an axis , and the CHAPTER I Exposition of ...
Page 2
Duncan Farquharson Gregory. Any fixed line is called an axis , and the three fixed in- tersecting lines are called the coordinate axes , their point of intersection being named the origin . Each of these lines may be considered as ...
Duncan Farquharson Gregory. Any fixed line is called an axis , and the three fixed in- tersecting lines are called the coordinate axes , their point of intersection being named the origin . Each of these lines may be considered as ...
Page 9
... fixed axis , the point where the 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 ...
... fixed axis , the point where the 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 ...
Page 11
... fixed points PQ , connected by a straight line , we have any number of points PQP , Q , ( fig . 5 ) connected by straight lines PQ , QP , PQ1 , and if from P , Q , P1 Qv we draw on AB the perpendiculars PM , QN , PM , Q1N ,, the whole ...
... fixed points PQ , connected by a straight line , we have any number of points PQP , Q , ( fig . 5 ) connected by straight lines PQ , QP , PQ1 , and if from P , Q , P1 Qv we draw on AB the perpendiculars PM , QN , PM , Q1N ,, the whole ...
Page 21
... fixed point in the indefinite straight line AP ( fig . 11 ) , and let a , ß , y , be its coordinates . Let x , y , z , be the coordinates of any other point P in the line , and let l , m , n , be the cosines of the angles which the line ...
... fixed point in the indefinite straight line AP ( fig . 11 ) , and let a , ß , y , be its coordinates . Let x , y , z , be the coordinates of any other point P in the line , and let l , m , n , be the cosines of the angles which the line ...
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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...