Elements of Quaternions |
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Page ii
... Calculus ( Note B ) , but they are treated in the present work by an entirely new analysis : and , at least for space , their theory has been thereby much extended in the Chapter to which we next proceed . CHAPTER III . APPLICATIONS OF ...
... Calculus ( Note B ) , but they are treated in the present work by an entirely new analysis : and , at least for space , their theory has been thereby much extended in the Chapter to which we next proceed . CHAPTER III . APPLICATIONS OF ...
Page iii
... Calculus of Quaternions , at least so far as quo- tients of vectors are concerned , with numerous geometrical illustra- tions . Still there are a few investigations respecting circumscribed cones , imaginary intersections , and ...
... Calculus of Quaternions , at least so far as quo- tients of vectors are concerned , with numerous geometrical illustra- tions . Still there are a few investigations respecting circumscribed cones , imaginary intersections , and ...
Page iv
... Calculus , from its fundamental connexion with the number " Four , " are found to present themselves in the course of the work . SECTION 4. - On Equality of Quaternions ; and on the Plane of a Quaternion ,. · Pages . 112-117 SECTION 5 ...
... Calculus , from its fundamental connexion with the number " Four , " are found to present themselves in the course of the work . SECTION 4. - On Equality of Quaternions ; and on the Plane of a Quaternion ,. · Pages . 112-117 SECTION 5 ...
Page viii
... Calculus ; especially the four formulæ ( pp . 316 , 317 ) : V. YVẞa = aSẞy - ẞSya ; Vyẞa = aSẞy - ẞSya + ySaß ; pSaßy = aSẞyp + ßSyap + ySaßp ; ( D ) ( G ) pSaßy = VẞySap + VyaS3p + VaßSyp ; in which a , ẞ , y , p are any four vectors ...
... Calculus ; especially the four formulæ ( pp . 316 , 317 ) : V. YVẞa = aSẞy - ẞSya ; Vyẞa = aSẞy - ẞSya + ySaß ; pSaßy = aSẞyp + ßSyap + ySaßp ; ( D ) ( G ) pSaßy = VẞySap + VyaS3p + VaßSyp ; in which a , ẞ , y , p are any four vectors ...
Page x
... Calculus , although they do not gene- rally possess the elementary property , that the sum of the logarithms of two quaternions is equal to the logarithm of their product : this ap- parent paradox , or at least deviation from ordinary ...
... Calculus , although they do not gene- rally possess the elementary property , that the sum of the logarithms of two quaternions is equal to the logarithm of their product : this ap- parent paradox , or at least deviation from ordinary ...
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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