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angle assume axes axis becomes called centre chords circle coefficients combined condition cone consecutive consequently considered constant containing coordinates corresponding cosy curvature curve cylinder determined developable developable surface dF dF diametral differential direction direction-cosines director distance drawn dx dy dy dz eliminating ellipsoid equal equation evidently expression fixed formulŠ 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 preceding principal projection quantities ratios rectangular reduced relation represent respectively result satisfied second order sheet shew side sphere squares straight line substitute suppose surface taken tangent plane third values vanish variables zero
Page 16 - To express the area of a triangle in terms of the coordinates of its angular points.
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...