Elements of Quaternions

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Longmans, Green, & Company, 1866 - Quaternions - 762 pages

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Contents

130
569
a normal to a surface Some of the theorems or constructions
574
Krown right cone with rectifying line for its axis and with H for
575
which is at once the Locus of its osculating Circle and the Envelope
581
in which v TT and wws the vector of an arbitrary point
585
Pages
591
or p p+c¹a Y or Vap+ pVyp+VpVλpµ0
593
the section of the surface 1 made by the normal plane to the given
595
ferences are given to a very interesting Memoir by M de SaintVenant Sur
598
10
601
dence o one of these can be at once translated into Monges equa
604
is thus completely and generally determined without any such difficulty
621
with a small circle osculating thereto example spherical conic con
629
it is ultimately equal p 595 to the quarter of the deviation 397
634
in which 7 dp is a tangent to a line of curvature while dv pdp
641
in fact it is cut
642
a a in d a Second Exponential Transformation is obtained with
649
in S₁ may be thus decomposed into factors p 666
666
comp pp 300 459 662 671 672 and conversely that when this last symbol
669
14
671
foregoing theory for the case of a Central Quadric and especially
674
inverse function p+e1 where e is any scalar and thus by chang
676
tirely arbitrary the values of r may be thus expressed p 681
681
Umbilics of a central quadric
686
136
689
surface and R R1 R2 the three corresponding points near to each other
690
being 1D³p its normal and tangential components are found
694
700
700
The vector of the centre of the quadric represented by the equation fp 28ep const with fp Sppp is generally x¹ε
705
Arch with illustration by a diagram Fig 85 p 706
706
15
709
law of the Inverse Square 713717
713
so that
719
to become a tangent this Theorem of Hodographie Isochronism which
726
introducing the two new integrals p 729
729
884
735
made respecting any smallness of excentricities or inclinations p 736
736
connecting the two new vectors ƒ with each other they are con
738
comp the formula W3 in p xlvi by the symbolic and cubic equa
742
direction of the projection of the ray p on the tangent plane to
757
17
761
Smith 1853

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