Quaternions As the Result of Algebraic Operations

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^(«. /?. R)=^(>Sa:/? + Fa/?)r.
50. =>S. ;'7a^ = ->S. R7/?a. 61. =-, S-r(7/9a:+iS/?a).
52. =-SrPa.
53. ==-S. 3ar.
54. IS(a:ia2. • . A)n = (- l)«*S:(a'„ . . . «2ai).
55. Sal3r=SaVl3r.
56. =>S-aF/?;'=^. /?Fra:=ASfrFa/?.
57. A/?;' + ;'/?a=27a:/?;-=27;'^a.
58. 2VaPr =aPr -\-{ar^- arp-rap + raP) +rl^a. [57.
* See Appendix.
60 QUATERNIONS 59. 2Vai^r=(^(l^r+rl^)-(^r+r(^)l^+r(^^-^M- 60. =2(aSpr-I^S(^r+rS(^l^)' [26.
61. Vai^r-(^^^r=Va[^r-V'^^Pr' 62. =Va(^r-^M- 63. =V'aVpy.
64. =-pSra^-rSap. [60.
65. =-F.
... 7(/?r)«. [62, 25.
66. . -. 7-7(/?r)«=/5>Sf;'«-r>S^«/?. [64.
67. 7. (7a/?)7r^ = -r^^7a:/?+^>S. (7a, /?)r. [63, 64.
68. = - r^apd +dSa^r- [^6, 24.
69. V'(Val^)Vrd=+aS-I^Vrd-l^S-{Vrd)a, [66.
70. =aSl^r^-^Sard. [56.
71. DSa^r =(^S^r^ +^Srad + rSa^^. [68, 70.
72. 7-7a:/?7/?;' = ;'>S-(7a:^)/?-^>S:. R^«^. [67.
73. =r^pVa^-pSra^. [24, 56.
74. =^Spar. [^/?7a:^=0, 60.
75. A^a:/?;' = 7-7/?a7Q:r. [74.
76. ^Sapr=y-yrpyp^- [48, 75.
77. RSa^r=vvarVr[^.
78. (5 = - (tiSi^ +/>Sy^ +A;aS/c^). [71.
123.


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