Elements of Quaternions |
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Page iii
... It is shown , by consideration of an angle on a desk , or inclined plane , that the complex relation of one vector to another , in length and 106-110 · 110-112 in direction , involves generally a system of four numerical.
... It is shown , by consideration of an angle on a desk , or inclined plane , that the complex relation of one vector to another , in length and 106-110 · 110-112 in direction , involves generally a system of four numerical.
Page xv
... relation ( p . 562 ) , tan Ctan H , 3 4 ( V ) which osculates to the cone of chords , drawn from the given point P XV Pages . 554-559 In this Article , or Series , 397 , and indeed also in 396 and 398 , several re- ferences are given to ...
... relation ( p . 562 ) , tan Ctan H , 3 4 ( V ) which osculates to the cone of chords , drawn from the given point P XV Pages . 554-559 In this Article , or Series , 397 , and indeed also in 396 and 398 , several re- ferences are given to ...
Page xxviii
... relation ( N1 ′ ) . ( e ) . If any fixed value be assigned to t , the equation ( N1 ) then re- presents the section made by a plane through a ( p . 651 ) , which sec- tion is an ellipse if the surface be an ellipsoid , but an hyperbola ...
... relation ( N1 ′ ) . ( e ) . If any fixed value be assigned to t , the equation ( N1 ) then re- presents the section made by a plane through a ( p . 651 ) , which sec- tion is an ellipse if the surface be an ellipsoid , but an hyperbola ...
Page xxix
... relations of reciprocity ( comp . p . 483 ) ; and a simple geometrical interpretation may be assigned , for this last ... relation to the lines of curvature : and their locus , for a confocal system , is a developable surface ( p . 663 ) ...
... relations of reciprocity ( comp . p . 483 ) ; and a simple geometrical interpretation may be assigned , for this last ... relation to the lines of curvature : and their locus , for a confocal system , is a developable surface ( p . 663 ) ...
Page xliii
... relation , pdp - p'dp = 2Vydp ; being the conjugate of p , but not here equal to it . ( Y2 " ' ) ( d ) . Connexions ( pp . 702 , 703 ) of the Mixed Transformations in the last cited Section , with the known Modular and Umbilicar Gene ...
... relation , pdp - p'dp = 2Vydp ; being the conjugate of p , but not here equal to it . ( Y2 " ' ) ( d ) . Connexions ( pp . 702 , 703 ) of the Mixed Transformations in the last cited Section , with the known Modular and Umbilicar Gene ...
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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