An Elementary Treatise on Quaternions |
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Page xi
... seen in our northern latitudes , i.e. that opposite to the direc- tion of motion of the hands of a watch . In Sir W. Hamilton's great works the opposite is employed . The student will find no difficulty in passing from the one to the ...
... seen in our northern latitudes , i.e. that opposite to the direc- tion of motion of the hands of a watch . In Sir W. Hamilton's great works the opposite is employed . The student will find no difficulty in passing from the one to the ...
Page 1
... seen that if positive quantities were measured off in one direction along a fixed line , a useful and lawful convention enabled us to express negative quantities of the same kind by simply laying them off on the same line in the ...
... seen that if positive quantities were measured off in one direction along a fixed line , a useful and lawful convention enabled us to express negative quantities of the same kind by simply laying them off on the same line in the ...
Page 5
... seen that the sign of equality between vectors contains implicitly equality in length and parallelism in direction . So far we have extended the meaning of an algebraical symbol . And it is to be noticed that an equation between vectors ...
... seen that the sign of equality between vectors contains implicitly equality in length and parallelism in direction . So far we have extended the meaning of an algebraical symbol . And it is to be noticed that an equation between vectors ...
Page 6
... seen in another way if we remember that by adding the differences of the Cartesian coordinates of A and B , to those of the coordinates of B and C , we get those of the coordinates of A and C. Hence these cöordinates enter linearly into ...
... seen in another way if we remember that by adding the differences of the Cartesian coordinates of A and B , to those of the coordinates of B and C , we get those of the coordinates of A and C. Hence these cöordinates enter linearly into ...
Page 9
... seen ( § 25 ) it is equivalent to three numerical equations ; but , as these involve the indefinite quantity a , they are virtually equivalent to but two , as in ordinary Geometry of Three Dimensions . ' 29. ] A good illustration of ...
... seen ( § 25 ) it is equivalent to three numerical equations ; but , as these involve the indefinite quantity a , they are virtually equivalent to but two , as in ordinary Geometry of Three Dimensions . ' 29. ] A good illustration of ...
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Common terms and phrases
a₁ axes axis Cartesian centre of inertia Chapter circle cloth cone conjugate constant cöordinates coplanar curvature curve developable surface diameters differential direction drawn easily ellipsoid envelop equal evidently expression Extra fcap extremity fcap Find the equation Find the locus given equation given line given vectors gives Hamilton Hence hodograph integral intersection last section length linear and vector locus normal obviously once operator origin osculating osculating plane P₁ parabola parallel perpendicular properties quaternion radius rectangular represents result right angles rotation S.aßy Saß scalar scalar equations second order self-conjugate shew solution sphere spherical straight line suppose surface surface of revolution tangent plane Taylor's Theorem tensor theorem three vectors triangle unit-vectors Vaß vector function versor w₁ write written Τρ φρ