Elements of Quaternions |
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Page xv
... locus of tangents to the curve ( or by p . 568 to the cone of parallels already mentioned ) ; new right cone , with a new semiangle , C , connected with H by the relation ( p . 562 ) , tan Ctan H , 3 4 ( V ) which osculates to the cone ...
... locus of tangents to the curve ( or by p . 568 to the cone of parallels already mentioned ) ; new right cone , with a new semiangle , C , connected with H by the relation ( p . 562 ) , tan Ctan H , 3 4 ( V ) which osculates to the cone ...
Page xxi
... Locus of the Osculating Circle to a given curve in space , may be represented rigorously by the vector expression ( p . 600 ) , 8 W1 = Ps + rst , sin u + r2r , vers u ; ( C1 ) in which s and u are two independent scalar variables ...
... Locus of the Osculating Circle to a given curve in space , may be represented rigorously by the vector expression ( p . 600 ) , 8 W1 = Ps + rst , sin u + r2r , vers u ; ( C1 ) in which s and u are two independent scalar variables ...
Page xxiii
... Locus of the osculating Circle , to itself , into which by ( g ) the two branches ( 0 ) that Singular Line on of its general cusp - edge are . curte fused . xxiii Pages . ( t ) . Other applications of preceding formulæ might be given ...
... Locus of the osculating Circle , to itself , into which by ( g ) the two branches ( 0 ) that Singular Line on of its general cusp - edge are . curte fused . xxiii Pages . ( t ) . Other applications of preceding formulæ might be given ...
Page xxiv
... loci , whereof one is a plane ( P ' ) . But usually the foregoing method requires , as in 398 , ( h ) ) , the solution of ... locus of the vertex of a quadric cone , which passes through six given points of space , A , B , C , D , E , F ...
... loci , whereof one is a plane ( P ' ) . But usually the foregoing method requires , as in 398 , ( h ) ) , the solution of ... locus of the vertex of a quadric cone , which passes through six given points of space , A , B , C , D , E , F ...
Page xxviii
... locus , as well as of the first system ( ƒ ) , but which have their centres on the line a ' , and are projected into circles , on a plane per- pendicular to this latter line ( p . 649 ) . ( h ) . Equation of Confocals ( p . 652 ) , Vv ...
... locus , as well as of the first system ( ƒ ) , but which have their centres on the line a ' , and are projected into circles , on a plane per- pendicular to this latter line ( p . 649 ) . ( h ) . Equation of Confocals ( p . 652 ) , Vv ...
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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