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aSpp axes axis Calculus Cartesian circle commutative law cone conjugate constant coordinates coplanar course curve diameters differential direction drawn easily ellipsoid equal equivalent evidently extremity factors Find the equation Find the locus formula geometrical given equation given lines given point given vectors gives Hamilton Hence hyperbola indeterminate intersection inverse function LAOB last section length linear and vector multiply obviously once operating origin osculating plane P. G. TAIT parabola parallel perpendicular proof properties proposition proved quaternion radius rectangular represented result right angles rotation S.apy scalar equations second order self-conjugate shew sides Similarly solution sphere spherical conic spherical excess straight line student suppose surface tangent plane Taylor's Theorem tensor theorem three vectors tion transformation triangle unit-vector vanish vector function vector perpendicular versor whence write written
Page 155 - Find the locus of a point the ratio of whose distances from two given points is constant. Let the given points be 0 and A, the extremities of the vector a.
Page 219 - Differentiation of the equations gives us 3p + q+l equations, linear and homogeneous in the 3m + n differentials of the scalar parameters, so that by the elimination of these we have one final scalar equation in the first case, two in the second ; and thus in each case we have just equations enough to eliminate all the arbitrary parameters.
Page 16 - The bisectors of the sides of a triangle meet in a point, which trisects each of them.
Page 197 - Find the equation of the locus of a point the square of whose distance from a given line is proportional to its distance from a given plane.
Page 52 - It is curious to compare the properties of these quaternion symbols with those of the Elective Symbols of Logic, as given in BOOLE'S wonderful treatise on the Laws of Thought ; and to think that the same grand science of mathematical analysis, by processes remarkably similar to each other, reveals to us truths in the science of position far beyond the powers of the geometer, and truths of deductive reasoning to which unaided thought could never have led the logician.