Elements of Quaternions |
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Page xv
... condition of developability of surface of emanants , ARTICLE 397. - Properties depending on the cube ( s3 ) of the are ; Radius r ( denoted here , for distinction , by a roman letter ) , and Vector rr , of Second Curvature ; this radius ...
... condition of developability of surface of emanants , ARTICLE 397. - Properties depending on the cube ( s3 ) of the are ; Radius r ( denoted here , for distinction , by a roman letter ) , and Vector rr , of Second Curvature ; this radius ...
Page xxii
... condition of coinci- dence ( o ) ; one of these can be at once translated into Monge's equa- tion of condition ( p . 603 ) , or into an equation slightly more general , as leaving the independent variable arbitrary ; but a simpler and ...
... condition of coinci- dence ( o ) ; one of these can be at once translated into Monge's equa- tion of condition ( p . 603 ) , or into an equation slightly more general , as leaving the independent variable arbitrary ; but a simpler and ...
Page xxiii
... condition of coincidence ( p ) is satisfied , the Surface is , as in ( n ) , at once the Enve- lope of the osculating Sphere and the Locus of the osculating Circle , to itself , into which by ( g ) the two branches ( 0 ) that Singular ...
... condition of coincidence ( p ) is satisfied , the Surface is , as in ( n ) , at once the Enve- lope of the osculating Sphere and the Locus of the osculating Circle , to itself , into which by ( g ) the two branches ( 0 ) that Singular ...
Page xxix
... Condition of Contact , of the same surface with the right line PP ' , ( ƒ ( p , p ' ) − 1 ) 3 = ( ƒp − 1 ) ( ƒp ' − 1 ) ; ( Q1 ) this latter is also a form of the equation of the Cone , with vertex at P. which is circumscribed to the ...
... Condition of Contact , of the same surface with the right line PP ' , ( ƒ ( p , p ' ) − 1 ) 3 = ( ƒp − 1 ) ( ƒp ' − 1 ) ; ( Q1 ) this latter is also a form of the equation of the Cone , with vertex at P. which is circumscribed to the ...
Page xxxi
... condition that each is perpendicular to its own conjugate , with respect to that indicating curve : the equation of such conjugation , of two tangents and r ' , being in the present notation ( see again p . 668 ) , STOT ' = 0 , or Sr'pr ...
... condition that each is perpendicular to its own conjugate , with respect to that indicating curve : the equation of such conjugation , of two tangents and r ' , being in the present notation ( see again p . 668 ) , STOT ' = 0 , or Sr'pr ...
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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