An Elementary Treatise on Quaternions, |
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Common terms and phrases
a₁ axis Cartesian Chapter circle cone conjugate constant cöordinates coplanar curvature curve developable surface diameters differential direction drawn easily ellipsoid envelop equal evidently expression Find the equation Find the locus formula geometry given equation given lines given point given vectors gives Hamilton Hence hyperbola indeterminate intersection inverse function last section length linear and vector multiply normal obviously origin osculating plane P₁ parabola parallel perpendicular properties prove quaternion radius rectangular represents right angles rotation S.aßy Sapa Saß scalar scalar equations second order self-conjugate sides solution sphere spherical conic ẞ² straight line student surface surface of revolution t₁ tangent plane Taylor's Theorem tensor theorem three vectors triangle unit-vector Vaß vector function vector perpendicular versor written φρ
Popular passages
Page 153 - 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 174 - The locus of the middle points of a system of parallel chords in a parabola is called a diameter.
Page 72 - Law: cos a = cos b cos c + sin b sin c cos A cos b = cos c cos a + sin c sin a cos B cos c = cos a cos b + sin a sin b cos C cos A = -cos B...
Page 195 - 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. 28. Show that the locus of the pole of the plane Sap = 1, with respect to the surface Sp<f' P = l, is a sphere, if a be subject to the condition Sa<p-'a = 0.
Page 149 - Find the locus of a point the sum of the squares of whose distances from two given points is constant.
Page 217 - To find the locus of the foot of the perpendicular drawn from the origin to a tangent plane to any surface.