Elements of Quaternions |
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Page vii
... Interpreting a Product of Two Vectors as a Quaternion , SECTION 2. - On some Consequences of the foregoing Inter- pretation , . • This first interpretation treats the product ß . a , as equal to the quotient 3 : a - 1 ; where a1 ( or Ra ) ...
... Interpreting a Product of Two Vectors as a Quaternion , SECTION 2. - On some Consequences of the foregoing Inter- pretation , . • This first interpretation treats the product ß . a , as equal to the quotient 3 : a - 1 ; where a1 ( or Ra ) ...
Page ix
... interpreting a Product or Function of Vectors as a Quaternion ; and on the Consistency of the Results of the Interpretation so ob- tained , with those which have been deduced from the two preceding Methods of the present Book , ix Pages ...
... interpreting a Product or Function of Vectors as a Quaternion ; and on the Consistency of the Results of the Interpretation so ob- tained , with those which have been deduced from the two preceding Methods of the present Book , ix Pages ...
Page xxiii
... interpreted by that illustrious analyst . The general integral here fund presents itself at first in a quaternion form ( p . 609 ) , but is easily translated ( p . 610 ) into the usual language of analysis . A less ge- seral integral is ...
... interpreted by that illustrious analyst . The general integral here fund presents itself at first in a quaternion form ( p . 609 ) , but is easily translated ( p . 610 ) into the usual language of analysis . A less ge- seral integral is ...
Page 8
... interpreted as in algebra . Thus , Oa = 0 , the zero on the one side denoting a null coefficient , and the zero on the other side denoting a null vector ; because by the rule , la + Oa = ( 1 + 0 ) a = la = a , and . ' . Oa = a - a = 0 ...
... interpreted as in algebra . Thus , Oa = 0 , the zero on the one side denoting a null coefficient , and the zero on the other side denoting a null vector ; because by the rule , la + Oa = ( 1 + 0 ) a = la = a , and . ' . Oa = a - a = 0 ...
Page 9
... interpreted as above , represents always a vector ß , which has the same direction as the multiplicand - line a , if x > 0 , but has the opposite direction if x < 0 , becoming null if x = 0. Conversely , if a and ẞ be any two actual ...
... interpreted as above , represents always a vector ß , which has the same direction as the multiplicand - line a , if x > 0 , but has the opposite direction if x < 0 , becoming null if x = 0. Conversely , if a and ẞ be any two actual ...
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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