An Elementary Treatise on Quaternions |
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Page vii
... constantly aimed at avoiding too great extension ; and in pursuance of this object have omitted many valuable elementary portions of the subject . One of these , the treatment of Quaternion logarithms and exponentials , I greatly regret ...
... constantly aimed at avoiding too great extension ; and in pursuance of this object have omitted many valuable elementary portions of the subject . One of these , the treatment of Quaternion logarithms and exponentials , I greatly regret ...
Page ix
... constant thought in its applications , would also be of great benefit . With it there can be no " shut your eyes , and write down your equations , " for mere mechanical dexterity of analysis is certain to lead at once to error on ...
... constant thought in its applications , would also be of great benefit . With it there can be no " shut your eyes , and write down your equations , " for mere mechanical dexterity of analysis is certain to lead at once to error on ...
Page xix
... constant , contains the whole theory of the motion of a rigid body with one point fixed . Reduction to the ordinary form dt dw dx dy dz = = = 2 W X Y Ꮓ Here , if no forces act , W , X , Y , Z are homogeneous functions of the third ...
... constant , contains the whole theory of the motion of a rigid body with one point fixed . Reduction to the ordinary form dt dw dx dy dz = = = 2 W X Y Ꮓ Here , if no forces act , W , X , Y , Z are homogeneous functions of the third ...
Page 1
... constantly employed in Analytical Geometry and Applied Mathematics . 3. ] Wallis , towards the end of the seventeenth century , proposed to represent the impossible roots of a quadratic equation by going out of the line on which , if ...
... constantly employed in Analytical Geometry and Applied Mathematics . 3. ] Wallis , towards the end of the seventeenth century , proposed to represent the impossible roots of a quadratic equation by going out of the line on which , if ...
Page 12
... constant . = ( e . ) To find the centre of inertia of any system . If OA = a , OB a1 , be the vector sides of any triangle , the vector from the vertex dividing the base AB in C so that BC : CA :: m : m1 is ma + 12 [ 31 . QUATERNIONS .
... constant . = ( e . ) To find the centre of inertia of any system . If OA = a , OB a1 , be the vector sides of any triangle , the vector from the vertex dividing the base AB in C so that BC : CA :: m : m1 is ma + 12 [ 31 . QUATERNIONS .
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Common terms and phrases
a₁ axes axis Cartesian centre of inertia Chapter circle cloth cone conjugate constant cöordinates coplanar curvature curve developable surface diameters differential direction drawn easily ellipsoid envelop equal evidently expression Extra fcap extremity fcap Find the equation Find the locus given equation given line given vectors gives Hamilton Hence hodograph integral intersection last section length linear and vector locus normal obviously once operator origin osculating osculating plane P₁ parabola parallel perpendicular properties quaternion radius rectangular represents result right angles rotation S.aßy Saß scalar scalar equations second order self-conjugate shew solution sphere spherical straight line suppose surface surface of revolution tangent plane Taylor's Theorem tensor theorem three vectors triangle unit-vectors Vaß vector function versor w₁ write written Τρ φρ