Elements of Quaternions |
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Page iii
... differentials ( of vectors and scalars ) is proposed , which is afterwards extended to differentials of quaternions , and which is in- dependent of developments and of infinitesimals , but involves the conception of limits . Vectors of ...
... differentials ( of vectors and scalars ) is proposed , which is afterwards extended to differentials of quaternions , and which is in- dependent of developments and of infinitesimals , but involves the conception of limits . Vectors of ...
Page x
... DIFFERENTIALS AND DEVELOPMENTS OF FUNCTIONS OF QUA- TERNIONS ; AND ON SOME APPLICATIONS OF QUATERNIONS TO GEOMETRICAL AND ... Differential Calculus of Quaternions in the next Chapter ( III . ii . ) , and to the Geometrical and other ...
... DIFFERENTIALS AND DEVELOPMENTS OF FUNCTIONS OF QUA- TERNIONS ; AND ON SOME APPLICATIONS OF QUATERNIONS TO GEOMETRICAL AND ... Differential Calculus of Quaternions in the next Chapter ( III . ii . ) , and to the Geometrical and other ...
Page xi
... differentials are not ne- cessarily , nor even generally , small . But it is shown at a later stage ( Art . 401 , pp ... differential of the reciprocal of a quaternion ( or vector ) , is also very often useful ; and so are the equations ...
... differentials are not ne- cessarily , nor even generally , small . But it is shown at a later stage ( Art . 401 , pp ... differential of the reciprocal of a quaternion ( or vector ) , is also very often useful ; and so are the equations ...
Page xxiv
... differential of the radius ( r ) of second curvature , divided by the differential of the are ( s ) . And the three common sides , PE , PE , PE " , of these two cones , which remain when the tangent PT is excluded , and of which one at ...
... differential of the radius ( r ) of second curvature , divided by the differential of the are ( s ) . And the three common sides , PE , PE , PE " , of these two cones , which remain when the tangent PT is excluded , and of which one at ...
Page xxvi
... differentials ( which have hitherto been finite , comp . p . xi . ) as infinitesimals ; * new deductions of osculating ... differential symbols , dp , d3p , & c . , as if they represented infinitely small differences , Ap , A2p , & c ...
... differentials ( which have hitherto been finite , comp . p . xi . ) as infinitesimals ; * new deductions of osculating ... differential symbols , dp , d3p , & c . , as if they represented infinitely small differences , Ap , A2p , & c ...
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Common terms and phrases
ABCD algebra angle anharmonic axis centre CHAP circle coefficients collinear comp Compare the Note complanar cone conic conjugate considered construction curvature curve cyclic deduced denote derived differential diplanar direction ellipsoid equal equation expression formula four fourth proportional function geometrical given plane given points harmonic conjugate imaginary interpreted intersection length line oa linear locus multiplication negative notation osculating osculating circle osculating plane P₁ parallelogram perpendicular positive quadratic quadrilateral quinary radius reciprocal relative direction represented right line right quaternions right quotient right versors roots rotation round scalar SECTION sides sphere spherical spherical angle sub-articles supposed surface symbol tangent tensor ternion theorem tion triangle ABC twisted cubic variable vector VIII whence whereof write