The Outlines of QuaternionsLongmans, Green, 1894 - 190 páginas |
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Página vii
... , y , 8 terminate in a plane ; then h + l + m + n = 0 . • 27 • · 28 29 39 ° . Equation of a plane in terms of its intercepts on the Cartesian axes of coordinates . PART II DIVISION AND MULTIPLICATION OF TWO VECTORS CHAPTER I CONTENTS vii.
... , y , 8 terminate in a plane ; then h + l + m + n = 0 . • 27 • · 28 29 39 ° . Equation of a plane in terms of its intercepts on the Cartesian axes of coordinates . PART II DIVISION AND MULTIPLICATION OF TWO VECTORS CHAPTER I CONTENTS vii.
Página viii
Henry William Lovett Hime. PART II DIVISION AND MULTIPLICATION OF TWO VECTORS CHAPTER I FIRST PRINCIPLES OF QUATERNIONS SECTION 1 Definitions ART . PAGE 1 ° . ( a ) Definition of a quaternion 30 ( b ) α - 1 99 99 30 = В = " B ; if q ' qa ...
Henry William Lovett Hime. PART II DIVISION AND MULTIPLICATION OF TWO VECTORS CHAPTER I FIRST PRINCIPLES OF QUATERNIONS SECTION 1 Definitions ART . PAGE 1 ° . ( a ) Definition of a quaternion 30 ( b ) α - 1 99 99 30 = В = " B ; if q ' qa ...
Página ix
... multiplication is not commutative 50 22 ° . Saß = ( aß + ßa ) ; Vaß = 1 ( aß — Ba ) . 50 23 ° . If Vq o , the constituent vectors are parallel 24 ° . The square of a vector is a negative scalar 50 51 ART . 25 ° . If Sq = o , CONTENTS ix.
... multiplication is not commutative 50 22 ° . Saß = ( aß + ßa ) ; Vaß = 1 ( aß — Ba ) . 50 23 ° . If Vq o , the constituent vectors are parallel 24 ° . The square of a vector is a negative scalar 50 51 ART . 25 ° . If Sq = o , CONTENTS ix.
Página x
... multiplication is not commu- tative . 58 ( c ) 99 37 ° . ( a + B ) 2 α αγ α ; β = B B В ( b ) Vector multiplication is distributive = associative a2 ± 2Saß + B2 , & c . , & c . 38 ° . Yax αβ αβ αβ β βγ βγ 58 • 59 99 " " 60 # 60 39 ...
... multiplication is not commu- tative . 58 ( c ) 99 37 ° . ( a + B ) 2 α αγ α ; β = B B В ( b ) Vector multiplication is distributive = associative a2 ± 2Saß + B2 , & c . , & c . 38 ° . Yax αβ αβ αβ β βγ βγ 58 • 59 99 " " 60 # 60 39 ...
Página xi
... = VΣq ; ΣKq = KZq , & c . , & c . 77 78 79 80 CHAPTER VIII MULTIPLICATION AND DIVISION OF TWO QUATERNIONS SECTION 1 57 ° . 192 4 . 92 = a quaternion = 99 99 Diplanar Quaternions 81 81 = Tq1 ; 92 Tq2 60 ° . Sqr ART CONTENTS xi.
... = VΣq ; ΣKq = KZq , & c . , & c . 77 78 79 80 CHAPTER VIII MULTIPLICATION AND DIVISION OF TWO QUATERNIONS SECTION 1 57 ° . 192 4 . 92 = a quaternion = 99 99 Diplanar Quaternions 81 81 = Tq1 ; 92 Tq2 60 ° . Sqr ART CONTENTS xi.
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Términos y frases comunes
arcs axis bisects centre chord circle coinitial vectors collinear commutative law conic conjugate consequently coplanar coplanar quaternions Crown 8vo diameter differential diplanar direction equal equation geometric given Hence hyperbola Illustrations intersection latus rectum Let OA locus mean point mẞ Multiplying OABC operation opposite P₁ parabola parallel parallelopiped perpendicular plane AOB positive or negative reciprocal right angles right quaternion right versors rotation Saß Saßy scalar Scientific Works published Similarly sphere SrVq ẞa symbols tangent TaTẞ tensor three vectors triangle Tẞ TẞTa unit-vector variable Vaß vector versor vertex VqVr VrVq Vẞy Woodcuts α α αβ β α βα φρ ОА ов ос тв وو ᎢᏰ
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