An Elementary Treatise on Quaternions |
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Page viii
... becomes identical with the Cartesian one . Nothing there- fore is ever lost , though much is generally gained , by employing Quaternions in preference to ordinary methods . In fact , even when Quaternions degrade to scalars , they give ...
... becomes identical with the Cartesian one . Nothing there- fore is ever lost , though much is generally gained , by employing Quaternions in preference to ordinary methods . In fact , even when Quaternions degrade to scalars , they give ...
Page 2
... becomes -ba√1 ; and now , of course , denotes the point whose x and y cöordinates are -b and a ; or the line joining this point with the origin . The length is still a2 + b2 , but the angle the line makes with the axis of a is tan - 1 ...
... becomes -ba√1 ; and now , of course , denotes the point whose x and y cöordinates are -b and a ; or the line joining this point with the origin . The length is still a2 + b2 , but the angle the line makes with the axis of a is tan - 1 ...
Page 25
... becomes equal to that of OB . For this only one number is required , viz . the ratio of the lengths of the two ... become The equation W= between two vectors, is equivalent to three distinct equations among numbers § -PRODUCTS AND ...
... becomes equal to that of OB . For this only one number is required , viz . the ratio of the lengths of the two ... become The equation W= between two vectors, is equivalent to three distinct equations among numbers § -PRODUCTS AND ...
Page 26
Peter Guthrie Tait. we see that the two vectors now coincide or become identical . To specify this operation three more numbers are required , viz . two angles ( such as node and inclina- tion in the case of a planet's orbit ) to fix the ...
Peter Guthrie Tait. we see that the two vectors now coincide or become identical . To specify this operation three more numbers are required , viz . two angles ( such as node and inclina- tion in the case of a planet's orbit ) to fix the ...
Page 28
... becomes a versor ( the tensor being unity ) and may be represented indifferently by any one of an infinite number of arcs of given length lying on the circumference of a circle , of which the two vectors are radii . This is of ...
... becomes a versor ( the tensor being unity ) and may be represented indifferently by any one of an infinite number of arcs of given length lying on the circumference of a circle , of which the two vectors are radii . This is 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