## 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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angle assume axes axis becomes called centre chords circle coefficients combined condition cone consecutive consequently considered constant coordinates corresponding curvature curve cylinder determined developable developable surface dF dF diameters differential direction direction-cosines director distance drawn dx dy dy dz eliminate ellipsoid equal equation evidently expression fixed formula function given gives Hence homogeneous function hyperboloid independent infinite intersection involving locus means meets Multiplying negative normal obtain origin parallel parameters pass perpendicular positive preceding principal projection quantities Qy² radius ratios reduced relation represent respectively result Rz² satisfied second order shew side sphere squares straight line substitute suppose surface taken tangent plane third values vanish variables zero

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Page 16 - To express the area of a triangle in terms of the coordinates of its angular points.

Page 309 - SOLUTIONS of the GEOMETRICAL PROBLEMS proposed at St. John's College, Cambridge, from 1830 to 1846, consisting chiefly of Examples in Plane Coordinate Geometry. With an Appendix, containing several general Properties of Curves of the Second Order...

Page 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.

Page 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.

Page 309 - Elementary Course of Mathematics. Designed principally for Students of the University of Cambridge. By HARVEY GOODWIN, DD, Lord Bishop of Carlisle.

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 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...