An Elementary Treatise on Quaternions |
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Page vii
... one among many methods he has employed ; and it is also the foundation of a memoir by M. Allégret , entitled Essai sur le Calcul des Quaternions ( Paris , 1862 ) . dy d is not equal to cos.log.æ , or that PREFACE . vii.
... one among many methods he has employed ; and it is also the foundation of a memoir by M. Allégret , entitled Essai sur le Calcul des Quaternions ( Paris , 1862 ) . dy d is not equal to cos.log.æ , or that PREFACE . vii.
Page viii
... equal to ( cos x ) 2 , while cos - 1a is not equal to ( cos x ) -1 . No such incongruities appear in Quaternions ; but what is true of operators and functions in other methods , that they are not generally commutative , is in ...
... equal to ( cos x ) 2 , while cos - 1a is not equal to ( cos x ) -1 . No such incongruities appear in Quaternions ; but what is true of operators and functions in other methods , that they are not generally commutative , is in ...
Page 5
... equal to AB depend in the same way upon the same three . Hence , all lines which are equal and parallel may be represented by a common symbol , and that symbol contains three distinct numbers . In this sense a line is called a VECTOR ...
... equal to AB depend in the same way upon the same three . Hence , all lines which are equal and parallel may be represented by a common symbol , and that symbol contains three distinct numbers . In this sense a line is called a VECTOR ...
Page 10
... can be constructed , whose sides are parallel , and equal , to the bisectors of the sides of any triangle . Let ABC be any triangle , Aa , Bb , Ce the bisectors of the sides . Then Aa = AB + Ba = AB + 1⁄2 10 [ 31 . QUATERNIONS .
... can be constructed , whose sides are parallel , and equal , to the bisectors of the sides of any triangle . Let ABC be any triangle , Aa , Bb , Ce the bisectors of the sides . Then Aa = AB + Ba = AB + 1⁄2 10 [ 31 . QUATERNIONS .
Page 11
... equal , to the sides taken in order BC , CA , AB ; the equation of Bb is ( § 28 ( 1 ) ) x 1/2 p = y + x ( y + 2 ) = ( 1 + x ) y + B. That of Cc is , in the same way , y P = — ( 1 + y ) B — 32 y . At the point 0 , where Bb and Ce ...
... equal , to the sides taken in order BC , CA , AB ; the equation of Bb is ( § 28 ( 1 ) ) x 1/2 p = y + x ( y + 2 ) = ( 1 + x ) y + B. That of Cc is , in the same way , y P = — ( 1 + y ) B — 32 y . At the point 0 , where Bb and Ce ...
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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