Elements of Quaternions

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

corresponding to 8 on tho corresponding sheet of tho Reciprocal comp
38
wy to principal terms pp 598 599 we have the expressions
47
tegrabttity of the equation Yj is expressed by the very simple for
70
noted by P geometrical constructions for this quantity P are assigned
86
circle are + 20 20 and 0 + 30 80 as illustrated by Fig
88
with others easily deduced whichmay all be illustrated by the above
89
a r+r
91
the last cited Section with the known Modular and Vmbilicar Gene
94
are rigorously proportional to the numbers1 and 3 the three forces
173
11
176
44
198
13
219
of reciprocity
222
may be mentioned
227
of the fire rectangular directions that each such generatrix rr is crossed perpendi
247
whereof the conjugate obtained by changing 1 to + 1 in the last
271
or p p + c1a Y or Yap + pVyp + XpVXpp 0 Y
278
and therefore ultimately p 600
310
in which u is a variable vector represents p 684 the normal plane
352
the four forces of the third group are proportional to 5 9 15
354
the independent variable being the arc in T while it is arbitrary
389
Again pp 560 561 if we write comp Art 396
396
so that by P p xii these three asymptotes compose a real and rect
406
F may be called the Principal Function and V the Characteristic
411
Remarks Introductory to this Concluding
495
On Normals and Tangent Planes to Surfaces 501510
501
of any central quadric
506
On Osculating Planes and Absolute Normals
511
curvatures of helix ellipse hyperbola logarithmic spiral
535
with a small circle osculating thereto example spherical conic con
541
defined as the limit of a sphere which contains the osculating circle
549

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