Elements of Quaternions |
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Page v
... Root ; General Reduction of a Quaternion in a given Plane , to a Standard Bino- mial Form , · SECTION 2. - On Continued Proportion of Four or more Vec- tors ; whole Powers and Roots of Quaternions ; and Roots of Unity , . 240-285 240 ...
... Root ; General Reduction of a Quaternion in a given Plane , to a Standard Bino- mial Form , · SECTION 2. - On Continued Proportion of Four or more Vec- tors ; whole Powers and Roots of Quaternions ; and Roots of Unity , . 240-285 240 ...
Page vi
... Roots , of any such Equation of the nth Degree , • SECTION 6. On the n2n Imaginary ( or Symbolical ) Roots of a Quaternion Equation of the nth Degree , with Coefficients of the kind considered in the foregoing Section , · SECTION 7 ...
... Roots , of any such Equation of the nth Degree , • SECTION 6. On the n2n Imaginary ( or Symbolical ) Roots of a Quaternion Equation of the nth Degree , with Coefficients of the kind considered in the foregoing Section , · SECTION 7 ...
Page xii
... roots , c1 , c2 , c3 ; while , in the same case , the vector equation , Τρφο = 0 , ( P ) is satisfied by a system of Three Real and Rectangular Directions : namely ( compare pp . 468 , 469 , and the Section III . iii . 7 ) , those of ...
... roots , c1 , c2 , c3 ; while , in the same case , the vector equation , Τρφο = 0 , ( P ) is satisfied by a system of Three Real and Rectangular Directions : namely ( compare pp . 468 , 469 , and the Section III . iii . 7 ) , those of ...
Page xx
... roots ẞ ( see again the last cited Section ) of the equation ( same p . 593 ) , Vẞoß = 0 : ( Z ) so that by ( P ) , p . xii . , these three asymptotes compose a real and rect- angular system , for the case of self - conjugation of the ...
... roots ẞ ( see again the last cited Section ) of the equation ( same p . 593 ) , Vẞoß = 0 : ( Z ) so that by ( P ) , p . xii . , these three asymptotes compose a real and rect- angular system , for the case of self - conjugation of the ...
Page xxxv
... roots , may be written ( p . 683 ) under the symbolical form , Sv ̄1 ( p + r ) ̄1v = 0 ; which may be developed ( same page ) into this other form , ( Y1 ) r2 + rSv1 xv + Sv -1 ¥ v = 0 , ( Y'1 ) the linear and vector functions , and x ...
... roots , may be written ( p . 683 ) under the symbolical form , Sv ̄1 ( p + r ) ̄1v = 0 ; which may be developed ( same page ) into this other form , ( Y1 ) r2 + rSv1 xv + Sv -1 ¥ v = 0 , ( Y'1 ) the linear and vector functions , and x ...
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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