Elements of Quaternions |
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Page iv
... called the scalar imaginary , in investigations re- specting non - real intersections , or non - real contacts , in geometry . SECTION 9. - On Vector - Arcs , and Vector - Angles , consi- dered as Representatives of Versors of ...
... called the scalar imaginary , in investigations re- specting non - real intersections , or non - real contacts , in geometry . SECTION 9. - On Vector - Arcs , and Vector - Angles , consi- dered as Representatives of Versors of ...
Page xv
... called the Rectifying Vector ; and if H denote the inclination ( considered first by Lancret ) , of this rectifying line ( ^ ) to the tangent ( 7 ) to the curve , then tan H - 1 tan Pr1r . ( V ' ) Krown right cone with rectifying line ...
... called the Rectifying Vector ; and if H denote the inclination ( considered first by Lancret ) , of this rectifying line ( ^ ) to the tangent ( 7 ) to the curve , then tan H - 1 tan Pr1r . ( V ' ) Krown right cone with rectifying line ...
Page xvii
... called here ( p . 581 ) the " Cir- cunscribed Developable being a surface analogous to the " Rectifying Developable " of Lancret , but belonging ( c ) to a higher order of ques- tions . And then , as the known angle H denotes ( 397 ) ...
... called here ( p . 581 ) the " Cir- cunscribed Developable being a surface analogous to the " Rectifying Developable " of Lancret , but belonging ( c ) to a higher order of ques- tions . And then , as the known angle H denotes ( 397 ) ...
Page xix
... called a Twisted Cubic : and this last curve , in virtue of its construction above described , and whatever the as- sumed direction of the auxiliary line PE may be , has contact of the fourth order ( or five - point contact ) with the ...
... called a Twisted Cubic : and this last curve , in virtue of its construction above described , and whatever the as- sumed direction of the auxiliary line PE may be , has contact of the fourth order ( or five - point contact ) with the ...
Page xxxv
... called the First Sheet , has the direction of the tangent to what may ( on the same plan ) be called the First Line of Curvature at P ; and the vector v of the point corresponding to s , on the corresponding sheet of the.
... called the First Sheet , has the direction of the tangent to what may ( on the same plan ) be called the First Line of Curvature at P ; and the vector v of the point corresponding to s , on the corresponding sheet of the.
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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