Elements of Quaternions

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

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Contents

c
44
37
45
ing e to p2 c new forms of the equation A6 of the wave
81
395 which osculates at the given point P this deviation by p 593
84
circle are + 20 20 and 0 + 30 30 as illustrated by Fig
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RiR21ri ra Tv95
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being followed by several subarticles which form with it a sort
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3
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245 184 246 266
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somewhat more briefly and perhaps more clearly than in the Lectures
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see again 408 e there pass three lines of curvature comp p 677
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366 333 411 310 370 334 412 311 373 335 414 312 374 336 416 337 417 338 420
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Pages
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59
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a
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470
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bodies earth and comet is the nearer to the sun results at sight from
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the same forms as before
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a is the vector at the time t of the mass or particle m P is the
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Su u o 25
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107
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in pp 550561 if we write comp Art 396
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it is ultimately equal p 595 to the quarter of the deviation 397
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653
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513
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and u is the small or large angle subtended at the centre K
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surface d is easily found p 738 to be represented by this other
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757
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m become thus
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149
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hich Y is a rector function of p not generally linear and deduced
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ěs SOME ADDITIONAL APPLICATIONs of QUATERNIoNs witH
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Section 30m Normals and Tangent Planes to Surfaces 501510
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SECTION 4On Osculating Planes and Absolute Normals
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the other it is found convenient to introduce two auxiliary vectors
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f║rences are given to a very interesting Memoir by M de SaintVenant Sur
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the ution of the surface 1 made by the normal plane to the given
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hence the curves of the first system n are Lines of Vibration of
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to a surface Some of the theorems or constructions
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bis 56 57
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therefore ultimately p 600
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which is at once the Locus of its osculating Circle and the Envelope
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of the same near point Ps from the osculating oircle at P multiplied
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bis 64
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dence one of these can be at once translated into Monges equa
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to the deviation ps PsSs of the given point p from the near sphere
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in fact it is cut
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with a small circle osculating thereto example spherical conic con
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Ši║n 6On Osculating Circles and Spheres to Curves
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397
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last cited Section with the known Modular and Umbilicar Gene
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in which w is a variable vector represents p 684 the normal plane
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in S1 may be thus decomposed into factors p 666
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foregoing theory for the case of a Central Quadric and especially
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Umbilics of a central quadric
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surface and R R1 R2 the three corresponding points near to each other
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t║ the very simple form p 692
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points s and x in which the axis of the osculating circle to the curve
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in which
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Arch with illustration by a diagram Fig 85 p 706
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and the laws of the centre of gravity of areas and of living force
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so that t and r are unit tangents to the lines of curvature it is easily
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measure of the force
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while in the second view of the same functions they satisfy the
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732
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the Sun on the Moon or of one Planet on another which is nearer
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fourth and subsequent groups by the same quaternion analysis
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connecting the two new vectors f with each other they are con
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are rigorously proportional to the numbers 1 and 3 the three forces
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comp the formula W3 in p xlvi by the symbolic and cubic equa
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80
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direction of the projection of the ray p on the tangent plane to
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projected on the normal v to the given surface the projection
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310 286 287 311 288 312 99 124 34 35 36 37
215
19
higher than the third order but that of R requires the fourth order of differen
20 343 344

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