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+ca Y or Vap+ pVyp+VpVλp0
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 1Dp 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 xε
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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