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 v
... means of symmetrical equations . The general advantage of symmetry in this branch of mathematics is so striking , that the utility of such a work will be at once recognized . There are undoubtedly many cases in which unsymmetrical ...
... means of symmetrical equations . The general advantage of symmetry in this branch of mathematics is so striking , that the utility of such a work will be at once recognized . There are undoubtedly many cases in which unsymmetrical ...
Page 1
... means of expressing by symbols , not only the absolute magnitudes of geometrical quan- tities , such as lines , areas , angles , & c . , but also the positions of points . Our habit of denoting arithmetical quantities by a single symbol ...
... means of expressing by symbols , not only the absolute magnitudes of geometrical quan- tities , such as lines , areas , angles , & c . , but also the positions of points . Our habit of denoting arithmetical quantities by a single symbol ...
Page 3
... means of determining the position of a point only within a limited portion of space . For , since the lines which intersect at O may be considered as infinite in length , the three planes , which by their intersection deter- mine these ...
... means of determining the position of a point only within a limited portion of space . For , since the lines which intersect at O may be considered as infinite in length , the three planes , which by their intersection deter- mine these ...
Page 9
... means of a straight line drawn parallel to a 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 ...
... means of a straight line drawn parallel to a 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 ...
Page 12
... means exactly similar to those employed in the case of several series of lines terminated at the same points , we may shew that if any number of straight lines be connected either by one plane area of which they are the boundaries , or ...
... means exactly similar to those employed in the case of several series of lines terminated at the same points , we may shew that if any number of straight lines be connected either by one plane area of which they are the boundaries , or ...
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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...