Elements of Quaternions |
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Page xv
... positive or ne- gatire ( whereas the radius r of first curvature is always treated as positive ) , and its reciprocal r1 may be thus expressed ( pp . 563 , 559 ) , Second Curvature * = r1 = S d3p Vdpd2p ' ( T ) , or , r1 = S S ( T ...
... positive or ne- gatire ( whereas the radius r of first curvature is always treated as positive ) , and its reciprocal r1 may be thus expressed ( pp . 563 , 559 ) , Second Curvature * = r1 = S d3p Vdpd2p ' ( T ) , or , r1 = S S ( T ...
Page 9
... ( positive or negative or null , whole numbers being included ) , and if a and ß be any two vectors , then ya ± xa = ( y + x ) a , ` y ( xa ) = ( yx ) a = yxa , x ( ẞ ± a ) = xẞ ± xa ; results which include those of Art . 13 , and may be ...
... ( positive or negative or null , whole numbers being included ) , and if a and ß be any two vectors , then ya ± xa = ( y + x ) a , ` y ( xa ) = ( yx ) a = yxa , x ( ẞ ± a ) = xẞ ± xa ; results which include those of Art . 13 , and may be ...
Page 55
... positive , for the particular arrangement of the points which is represented in the recent figure . 68. The formula III . may however be regarded as per- fectly general , if we agree to say that a pyramidal volume changes sign , or ...
... positive , for the particular arrangement of the points which is represented in the recent figure . 68. The formula III . may however be regarded as per- fectly general , if we agree to say that a pyramidal volume changes sign , or ...
Page 107
... positive or of the negative kind . For let z denote any such ( actual * ) scalar , and let a denote any ( actual ) vector ; then we have seen ( 15 ) that the product za denotes another ( actual ) vector , say B ' , which is either ...
... positive or of the negative kind . For let z denote any such ( actual * ) scalar , and let a denote any ( actual ) vector ; then we have seen ( 15 ) that the product za denotes another ( actual ) vector , say B ' , which is either ...
Page 108
... positive , then the positive axis of the rotation AOB , in Fig . 33 , must be conceived to be directed downward , or below the plane of the paper . CHAP . I. ] QUOTient of two vectors A QUATERNION 108 [ BOOK II . ELEMENTS OF QUATERNIONS .
... positive , then the positive axis of the rotation AOB , in Fig . 33 , must be conceived to be directed downward , or below the plane of the paper . CHAP . I. ] QUOTient of two vectors A QUATERNION 108 [ BOOK II . ELEMENTS OF QUATERNIONS .
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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