An Elementary Treatise on Quaternions |
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Page xiv
... length is ds . §§ 38 , 39 . Examples with solutions . §§ 40-44 . EXAMPLES TO CHAPTER I. • 22-24 CHAPTER II ... lengths , and directions , of B and a . § 50 . Reciprocal of a quaternion defined , B 1 α q gives or q " a q B ' 1 T.q - 1 Tq ...
... length is ds . §§ 38 , 39 . Examples with solutions . §§ 40-44 . EXAMPLES TO CHAPTER I. • 22-24 CHAPTER II ... lengths , and directions , of B and a . § 50 . Reciprocal of a quaternion defined , B 1 α q gives or q " a q B ' 1 T.q - 1 Tq ...
Page 1
... length , of lines . 2. ] Thus it was long ago seen that if positive quantities were measured off in one direction along a fixed line , a useful and lawful convention enabled us to express negative quantities of the same kind by simply ...
... length , of lines . 2. ] Thus it was long ago seen that if positive quantities were measured off in one direction along a fixed line , a useful and lawful convention enabled us to express negative quantities of the same kind by simply ...
Page 2
... length , of this line ; since , as b we see at once , the direction is inclined at an angle tan - 1 to the axis of a , and the length is √a2 + b2 . a 6. ] Operating on this symbol by the factor 1 , it becomes -ba√1 ; and now , of ...
... length , of this line ; since , as b we see at once , the direction is inclined at an angle tan - 1 to the axis of a , and the length is √a2 + b2 . a 6. ] Operating on this symbol by the factor 1 , it becomes -ba√1 ; and now , of ...
Page 5
... length to AB and if these lines be parallel , we have evidently CD = AB = a , where it will be seen that the sign of equality between vectors contains implicitly equality in length and parallelism in direction . So far we have extended ...
... length to AB and if these lines be parallel , we have evidently CD = AB = a , where it will be seen that the sign of equality between vectors contains implicitly equality in length and parallelism in direction . So far we have extended ...
Page 6
... between A and C , other- wise negative but such that its numerical value , independent of sign , is the ratio of the length of BC to that of AB . This is at once evident if AB and BC be commensurable ; 6 Co [ 20 . QUATERNIONS .
... between A and C , other- wise negative but such that its numerical value , independent of sign , is the ratio of the length of BC to that of AB . This is at once evident if AB and BC be commensurable ; 6 Co [ 20 . QUATERNIONS .
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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