Elements of Quaternions |
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Page iv
... Square of a Quaternion , . SECTION 8. - On the Versor of a Quaternion , or of a Vec- tor ; and on some General Formulæ of Transformation , 133-142 In the five foregoing Sections it is shown , among other things , that the plane of a ...
... Square of a Quaternion , . SECTION 8. - On the Versor of a Quaternion , or of a Vec- tor ; and on some General Formulæ of Transformation , 133-142 In the five foregoing Sections it is shown , among other things , that the plane of a ...
Page v
... Square 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 ...
... Square 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 ...
Page vii
... Square of a Vector is shown to be always a Negative Scalar , namely the negative of the square of the tensor of that vector , or of the number which expresses its length ; and some geometrical applications of this fertile principle , to ...
... Square of a Vector is shown to be always a Negative Scalar , namely the negative of the square of the tensor of that vector , or of the number which expresses its length ; and some geometrical applications of this fertile principle , to ...
Page xxxvii
... square , of the ( imaginary ) normal erected , is still to be made equal to the square of that semiaxis . 62 = φιν = φιφρ , for the vector of.
... square , of the ( imaginary ) normal erected , is still to be made equal to the square of that semiaxis . 62 = φιν = φιφρ , for the vector of.
Page xlvi
... square ( Ti2 ) of the semidiameter of the ellipsoid ( P3 ) , which has the direction of that axis ; and hence may be derived , with the help of the first general construc- tion of an ellipsoid , suggested by quaternions , a simple ...
... square ( Ti2 ) of the semidiameter of the ellipsoid ( P3 ) , which has the direction of that axis ; and hence may be derived , with the help of the first general construc- tion of an ellipsoid , suggested by quaternions , a simple ...
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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