An Elementary Treatise on Quaternions |
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Page xiii
... interpreted in plane rotation . § 8 . Curious speculation of Servois . § 11 . Elementary geometrical ideas connected ... interpretation of a vector as representing translation . § 19 . Definition of - . It simply reverses a vector . § 20 ...
... interpreted in plane rotation . § 8 . Curious speculation of Servois . § 11 . Elementary geometrical ideas connected ... interpretation of a vector as representing translation . § 19 . Definition of - . It simply reverses a vector . § 20 ...
Page xv
... ; a vector ; if quaternions are to deal with space indifferently in all directions . § 93 . EXAMPLES TO CHAPTER II . 46 , 47 CHAPTER III . - INTERPRETATIONS AND TRANSFORMATIONS OF QUATERNION EXPRESSIONS CONTENTS . XV.
... ; a vector ; if quaternions are to deal with space indifferently in all directions . § 93 . EXAMPLES TO CHAPTER II . 46 , 47 CHAPTER III . - INTERPRETATIONS AND TRANSFORMATIONS OF QUATERNION EXPRESSIONS CONTENTS . XV.
Page xvi
Peter Guthrie Tait. CHAPTER III . - INTERPRETATIONS AND TRANSFORMATIONS OF QUATERNION EXPRESSIONS If be the angle between two ... Interpretation of aßy when it is a vector . § 106 . Examples of variety in simple transformations . § 107 ...
Peter Guthrie Tait. CHAPTER III . - INTERPRETATIONS AND TRANSFORMATIONS OF QUATERNION EXPRESSIONS If be the angle between two ... Interpretation of aßy when it is a vector . § 106 . Examples of variety in simple transformations . § 107 ...
Page xviii
... interpretation of these results . §§ 162-166 . Proof of the transformation where Op = fp + hV . ( i + ek ) p ( i - ek ) ( 4 - g1 ) i = 0 , ( p — g1 ) k = 0 , € 2 92-93 = f = h - Another transformation is 91-93 , ( 91 + 9a ) , - ( 91-92 ) ...
... interpretation of these results . §§ 162-166 . Proof of the transformation where Op = fp + hV . ( i + ek ) p ( i - ek ) ( 4 - g1 ) i = 0 , ( p — g1 ) k = 0 , € 2 92-93 = f = h - Another transformation is 91-93 , ( 91 + 9a ) , - ( 91-92 ) ...
Page 8
... and a an indefinite number , represents the straight line drawn from the origin parallel to ẞ ( § 22 ) . = The straight line drawn from 4 , where OA 8 [ 26 . QUATERNIONS . De Moivre's Theorem interpreted in plane rotation §
... and a an indefinite number , represents the straight line drawn from the origin parallel to ẞ ( § 22 ) . = The straight line drawn from 4 , where OA 8 [ 26 . QUATERNIONS . De Moivre's Theorem interpreted in plane rotation §
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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