Elements of Quaternions |
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Page xiv
... ( comp . Art . 389 ) . The centre s , of the sphere so found , is ( as usual ) the point in which the polar axis ( Art . 391 ) touches the cusp - edge of the polar developable . Other general construction for the same centre ( p . 551 , comp ...
... ( comp . Art . 389 ) . The centre s , of the sphere so found , is ( as usual ) the point in which the polar axis ( Art . 391 ) touches the cusp - edge of the polar developable . Other general construction for the same centre ( p . 551 , comp ...
Page xxii
... ( comp . the Notes to pp . 602 , 603 , 609 , 610 of these Elements ) ; namely , to determine the envelope of a sphere with varying radius R , whereof the centre s traverses a given curve in space ; or briefly , to find the Envelope of a ...
... ( comp . the Notes to pp . 602 , 603 , 609 , 610 of these Elements ) ; namely , to determine the envelope of a sphere with varying radius R , whereof the centre s traverses a given curve in space ; or briefly , to find the Envelope of a ...
Page xxxvi
... ( comp . pp . 507 , 508 ) of the Surface of Centres , has ( by p . 684 ) the expres sion , V = T ( SPT ) 1 ; ( D2 ) which may also be considered ( comp . ( i ) ) to be a form of the Vector Equation of that Reciprocal Surface . ( k ) . The ...
... ( comp . pp . 507 , 508 ) of the Surface of Centres , has ( by p . 684 ) the expres sion , V = T ( SPT ) 1 ; ( D2 ) which may also be considered ( comp . ( i ) ) to be a form of the Vector Equation of that Reciprocal Surface . ( k ) . The ...
Page xxxviii
... ( comp . ( i ) ) , as a new Vector Form * of the Equation of the Surface of Centres , for the case ( o ) of a given central quadric . ( t ) . In connexion with the same expressions for σ1 , 2 , it may be observed that if ri , 2 be the ...
... ( comp . ( i ) ) , as a new Vector Form * of the Equation of the Surface of Centres , for the case ( o ) of a given central quadric . ( t ) . In connexion with the same expressions for σ1 , 2 , it may be observed that if ri , 2 be the ...
Page xxxix
... ( comp . pp . 685 , 689 ) , F2v = Svp21v = Sv ( p − 1 + r1 ) v ; ( R2 ) ( R2 " ) and accordingly ( comp . pp . 483 , 645 ) , we have F2v2 Fv = 1 , and ƒʊn = fr = r . ( 2 ) . For a line of second curvature on the given surface , the ...
... ( comp . pp . 685 , 689 ) , F2v = Svp21v = Sv ( p − 1 + r1 ) v ; ( R2 ) ( R2 " ) and accordingly ( comp . pp . 483 , 645 ) , we have F2v2 Fv = 1 , and ƒʊn = fr = r . ( 2 ) . For a line of second curvature on the given surface , 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