Introduction to Quaternions: With Numerous Examples |
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Page 6
... parallel , ' because we wish to guard the student against confounding ' vector AB ' with ' vector BA . ' 2. In order to apply algebra to geometry , it CHAPTER II VECTOR ADDITION AND SUBTRACTION 6-31 Definition of a VECTOR, with ...
... parallel , ' because we wish to guard the student against confounding ' vector AB ' with ' vector BA . ' 2. In order to apply algebra to geometry , it CHAPTER II VECTOR ADDITION AND SUBTRACTION 6-31 Definition of a VECTOR, with ...
Page 7
... parallel vectors are concerned , all the laws of Algebra must be applicable . Thus ( in Art . 1 ) AB + BC or a + a produces the same result as AC which is twice as great as AB , and is there- fore properly represented by 2a ; and so on ...
... parallel vectors are concerned , all the laws of Algebra must be applicable . Thus ( in Art . 1 ) AB + BC or a + a produces the same result as AC which is twice as great as AB , and is there- fore properly represented by 2a ; and so on ...
Page 9
... parallel . Let AB be equal and parallel to CD ; to prove that AC is equal and parallel to BD . Let vector AB be represented by a , then ( Art . 1 ) vector CD is also repre- c sented by a . D B If now vector CA be represented by ß ...
... parallel . Let AB be equal and parallel to CD ; to prove that AC is equal and parallel to BD . Let vector AB be represented by a , then ( Art . 1 ) vector CD is also repre- c sented by a . D B If now vector CA be represented by ß ...
Page 10
... parallel ; i.e. CA is equal and parallel to BD . Ex . 2. The opposite sides of a parallelogram are equal ; and the diagonals bisect each other . Since AB is parallel to CD , if vector AB be represented by a , vector CD will be ...
... parallel ; i.e. CA is equal and parallel to BD . Ex . 2. The opposite sides of a parallelogram are equal ; and the diagonals bisect each other . Since AB is parallel to CD , if vector AB be represented by a , vector CD will be ...
Page 11
... parallel to DE , and equal to 2DE . Again , BG + GABA = 2DE = 2 ( DG + GE ) . B A F E Now vector BG is along GE , and vector GA along DG . .. ( Art . 6 ) BG = 2GE , GA = 2DG , whence the same is true of the lines . Lastly , BG = 2BE ...
... parallel to DE , and equal to 2DE . Again , BG + GABA = 2DE = 2 ( DG + GE ) . B A F E Now vector BG is along GE , and vector GA along DG . .. ( Art . 6 ) BG = 2GE , GA = 2DG , whence the same is true of the lines . Lastly , BG = 2BE ...
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Common terms and phrases
ALGEBRA ARITHMETIC Assistant Master aßy axis BEGINNERS bisects Cambridge centre chord circle Clifton College cone CONIC SECTIONS conjugate diameters constant drawn Edited ELEMENTARY TREATISE ellipse ellipsoid ENGLISH equal EXAMPLES FASNACHT Fcap find the locus G. E. FASNACHT GEOMETRY given lines given point gives GRAMMAR GREEK Hence hyperbola Illustrated intersection Introduction and Notes ISAAC TODHUNTER J. P. MAHAFFY LATIN Lecturer LL.D M.A. Cr m₁ MACMILLAN'S Mathematics middle points Owens College p₁ parabola parallelepiped parallelogram PRIMER Prof Professor quaternion revised right angles rotation Sapa Saß scalar School shews squares strain tangent plane tetrahedron Translated triangle Trinity College unit vectors Vaß vector parallel vector perpendicular Vẞy whence yẞ αβγ φρ
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