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A treatise on the application of analysis to solid geometry. Commenced by D ...
Visualização completa - 1845
A Treatise on the Application of Analysis to Solid Geometry, Commenced by D ...
William Walton, Sir,Duncan Farquharson Gregory
Não há visualização disponível - 2016
angle assume axes axis becomes called centre chords circle coefficients combined condition cone consequently considered constant contain coordinates corresponding cosy curvature curve cylinder determined developable developable surface diametral plane differential direction direction-cosines director distance drawn eliminate ellipse ellipsoid equal equation evidently expression fixed formulæ function geometrical given gives Hence homogeneous function hyperbolic hyperboloid independent infinite intersection involving Let the equations locus means meets Multiplying negative normal obtain origin parallel parameters pass perpendicular positive possible preceding principal projection quantities ratios rectangular reduced referred relation represent respectively result satisfied second degree second order sheet shew side similar sphere squares straight line substitute suppose surface taken tangent plane third values vanish variables zero
Página 16 - To express the area of a triangle in terms of the coordinates of its angular points.
Página 309 - Mathematical Tracts on the Lunar and Planetary Theories. The Figure of the Earth, Precession and Nutation, the Calculus of Variations, and the Undulatory Theory of Optics.
Página 305 - 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.
Página 309 - Elementary Course of Mathematics. Designed principally for Students of the University of Cambridge. By HARVEY GOODWIN, DD, Lord Bishop of Carlisle.
Página 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.
Página 278 - 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...