Introduction to Quaternions |
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Page 55
... formula 2 ) ; Vẞy = a , a vector perpendicular to the plane OBC ; and since y ' , a ' are both perpendicular to OB , the line along which is the vector ß ; OB is perpendicular to the plane which passes through y , a ' , and therefore ...
... formula 2 ) ; Vẞy = a , a vector perpendicular to the plane OBC ; and since y ' , a ' are both perpendicular to OB , the line along which is the vector ß ; OB is perpendicular to the plane which passes through y , a ' , and therefore ...
Page 160
... formula 13 . aS . Byd - BS . yda + yS . daß 71. EXAMPLES . Ex . 1. To express the relation between the sides of a spherical triangle and the angles opposite to them . have Retaining the notation and figure of Ex . 2 , Art . 29 , we ...
... formula 13 . aS . Byd - BS . yda + yS . daß 71. EXAMPLES . Ex . 1. To express the relation between the sides of a spherical triangle and the angles opposite to them . have Retaining the notation and figure of Ex . 2 , Art . 29 , we ...
Page 161
... ( Formula 11 ) , therefore S. ( B - a ) V. Vẞy Vya = - ( SBy - Say ) S. Bya . Hence Now SBy = Say . - BC2 + OA3 = ( y − ß ) 2 + a2 2 = a2 + B2 + y2 - 2SBY = a2 + ß2 + y2 − 2Say = ( y - a ) 2 + B2 = AC2 + OB2 . Consequently the condition ...
... ( Formula 11 ) , therefore S. ( B - a ) V. Vẞy Vya = - ( SBy - Say ) S. Bya . Hence Now SBy = Say . - BC2 + OA3 = ( y − ß ) 2 + a2 2 = a2 + B2 + y2 - 2SBY = a2 + ß2 + y2 − 2Say = ( y - a ) 2 + B2 = AC2 + OB2 . Consequently the condition ...
Page 162
... formula 3 , S. ( 8 - yẞ ) ya = 0 , yS . Bya = S. Sya , yS . αβγ = S. δγα .... lastly , because O , A , B , c are in the same plane i . e . or S. ( 8 - zy ) aẞ = 0 , == 25. γαβ = 5 . δαβ , 25. αβγ = S. δαβ ....... ( 3 ) ; · ( 4 ) ...
... formula 3 , S. ( 8 - yẞ ) ya = 0 , yS . Bya = S. Sya , yS . αβγ = S. δγα .... lastly , because O , A , B , c are in the same plane i . e . or S. ( 8 - zy ) aẞ = 0 , == 25. γαβ = 5 . δαβ , 25. αβγ = S. δαβ ....... ( 3 ) ; · ( 4 ) ...
Page 164
... formula ( 11 ) , omitting the common factor S. aßy , ( -1 ) + ( - - ) n α + 1 + - γ . m From this expression the vectors of the intersections of the other planes may at once be written down . That of ABD , A'B'D ' is ( − 1 164 [ CHAP ...
... formula ( 11 ) , omitting the common factor S. aßy , ( -1 ) + ( - - ) n α + 1 + - γ . m From this expression the vectors of the intersections of the other planes may at once be written down . That of ABD , A'B'D ' is ( − 1 164 [ CHAP ...
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Common terms and phrases
A. S. WALPOLE A. W. VERRALL ALGEBRA ARITHMETIC Assistant Master aßy axis BEGINNERS bisects Cambridge centre chord circle cone CONIC SECTIONS conjugate diameters constant drawn Edited ELEMENTARY TREATISE ellipse ellipsoid ENGLISH equal EXAMPLES Exercises Fcap find the locus G. E. FASNACHT GEOMETRY given lines given point gives GRAMMAR GREEK Hence HISTORY hyperbola Illustrated intersection Introduction and Notes ISAAC TODHUNTER J. P. MAHAFFY LATIN Litt Litt.D LL.D M.A. BOOK M.A. Cr MACMILLAN'S Mathematics middle points parabola parallelepiped parallelogram PRIMER Prof Professor quaternion revised right angles rotation Sapa Saß scalar School shews Spop squares strain tangent plane tetrahedron Translated triangle Trinity College unit vectors values Vaß vector parallel vector perpendicular Vẞy whence yẞ αβγ φρ
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