An Elementary Treatise on Quaternions |
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Page viii
... solution 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 ...
... solution 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 ...
Page xiv
... solutions . § 31 . Differentiation of a vector , when given as a function of one number . §§ 32-38 . If the equation of a curve be P = $ ( 8 ) where s is the length of the arc , dp is a vector tangent to the curve , and its length is ds ...
... solutions . § 31 . Differentiation of a vector , when given as a function of one number . §§ 32-38 . If the equation of a curve be P = $ ( 8 ) where s is the length of the arc , dp is a vector tangent to the curve , and its length is ds ...
Page xvii
... SOLUTION OF EQUATIONS OF THE FIRST DEGREE . 77-100 The most general equation of the first degree in an unknown quaternion q , may be written ΣV.aqb + S.cq = d , where a , b , c , d are given quaternions . Elimination of Sq , and ...
... SOLUTION OF EQUATIONS OF THE FIRST DEGREE . 77-100 The most general equation of the first degree in an unknown quaternion q , may be written ΣV.aqb + S.cq = d , where a , b , c , d are given quaternions . Elimination of Sq , and ...
Page xviii
... solution of a quaternion equation— Examples . §§ 175-179 . The linear function of a quaternion is given by a symbolical biquadratic . § 180 . Particular forms of linear equations . §§ 181-183 . A quaternion equation of the mth degree in ...
... solution of a quaternion equation— Examples . §§ 175-179 . The linear function of a quaternion is given by a symbolical biquadratic . § 180 . Particular forms of linear equations . §§ 181-183 . A quaternion equation of the mth degree in ...
Page xx
... is one and but one solution of S. ( e2vu ) = 4 ′′ r . § 505 . MISCELLANEOUS EXAMPLES 288-296 ERRATUM . Page 102 , line 20 , for 44p - 4op_read_p ¥ ' p— ¥ o'p . QUATERNIONS . CHAPTER I. VECTORS , AND THEIR COMPOSITION . XX CONTENTS .
... is one and but one solution of S. ( e2vu ) = 4 ′′ r . § 505 . MISCELLANEOUS EXAMPLES 288-296 ERRATUM . Page 102 , line 20 , for 44p - 4op_read_p ¥ ' p— ¥ o'p . QUATERNIONS . CHAPTER I. VECTORS , AND THEIR COMPOSITION . XX CONTENTS .
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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