An Elementary Treatise on Quaternions |
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Page xiv
... sphere . § 53 . Versor multiplication illustrated by the composition of arcs . § 54 . Proof that K ( gr ) = Kr . Kq . § 55 . Proof of the Associative Law of Multiplication p.qr = pq.r. §§ 57-60 . [ Digression on Spherical Conics . § 59 ...
... sphere . § 53 . Versor multiplication illustrated by the composition of arcs . § 54 . Proof that K ( gr ) = Kr . Kq . § 55 . Proof of the Associative Law of Multiplication p.qr = pq.r. §§ 57-60 . [ Digression on Spherical Conics . § 59 ...
Page xvi
... spherical trigonometry . §§ 108-113 . Representation , graphic , and by quaternions , of the spherical excess . §§ 114 , 115 . Loci represented by different equations - points , lines , surfaces , and solids . §§ 116-119 . Proof that .1 ...
... spherical trigonometry . §§ 108-113 . Representation , graphic , and by quaternions , of the spherical excess . §§ 114 , 115 . Loci represented by different equations - points , lines , surfaces , and solids . §§ 116-119 . Proof that .1 ...
Page xviii
... SPHERE AND CYCLIC CONE . 120-132 EXAMPLES TO CHAPTER VII . . 132-134 CHAPTER VIII . - SURFACES OF THE SECOND ORDER . 135-151 · EXAMPLES TO CHAPTER VIII . 151-154 CHAPTER IX . - GEOMETRY OF CURVES AND SURFACES 155-186 xviii CONTENTS .
... SPHERE AND CYCLIC CONE . 120-132 EXAMPLES TO CHAPTER VII . . 132-134 CHAPTER VIII . - SURFACES OF THE SECOND ORDER . 135-151 · EXAMPLES TO CHAPTER VIII . 151-154 CHAPTER IX . - GEOMETRY OF CURVES AND SURFACES 155-186 xviii CONTENTS .
Page 29
... sphere , we can easily prove that quaternion multiplication is not generally commutative . or OB 04 Thus let ૧ be the versor AB Make BC = AB , ( which , it must be remembered , makes the points A , B , C lie in one great circle ) ...
... sphere , we can easily prove that quaternion multiplication is not generally commutative . or OB 04 Thus let ૧ be the versor AB Make BC = AB , ( which , it must be remembered , makes the points A , B , C lie in one great circle ) ...
Page 30
... Spherical Conics . As they are not usually familiar to students , we make a slight digression for the purpose of proving ... sphere . LEMMA . If a cone have one series of circular 30 [ 57 . QUATERNIONS . Proof of the Associative Law of ...
... Spherical Conics . As they are not usually familiar to students , we make a slight digression for the purpose of proving ... sphere . LEMMA . If a cone have one series of circular 30 [ 57 . QUATERNIONS . Proof of the Associative Law 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