Elements of Quaternions |
From inside the book
Results 1-5 of 100
Page iv
... four numerical elements . Many other motives , leading to the adoption of the name , " Quater- nion , " for the subject of the present Calculus , from its fundamental connexion with the number " Four , " are found to present themselves ...
... four numerical elements . Many other motives , leading to the adoption of the name , " Quater- nion , " for the subject of the present Calculus , from its fundamental connexion with the number " Four , " are found to present themselves ...
Page v
... four scalars , or ordinary algebraic quantities , while i , j , k are three new symbols , obeying the laws contained in the formula ( A ) , and therefore not subject to all the usual rules of alge- bra : since we have , for instance ...
... four scalars , or ordinary algebraic quantities , while i , j , k are three new symbols , obeying the laws contained in the formula ( A ) , and therefore not subject to all the usual rules of alge- bra : since we have , for instance ...
Page viii
... four formulæ ( pp . 316 , 317 ) : V. YVẞa = aSẞy - ẞSya ; Vyẞa = aSẞy - ẞSya + ySaß ; pSaßy = aSẞyp + ßSyap + ySaßp ; ( D ) ( G ) pSaßy = VẞySap + VyaS3p + VaßSyp ; in which a , ẞ , y , p are any four vectors , while S and V are signs ...
... four formulæ ( pp . 316 , 317 ) : V. YVẞa = aSẞy - ẞSya ; Vyẞa = aSẞy - ẞSya + ySaß ; pSaßy = aSẞyp + ßSyap + ySaßp ; ( D ) ( G ) pSaßy = VẞySap + VyaS3p + VaßSyp ; in which a , ẞ , y , p are any four vectors , while S and V are signs ...
Page 20
... four points O , A , B , C , by any system of pa- rallel ordinates , into four other A points , o , A , B , C , on any as- sumed plane , the sum of the three projected vectors , a , ẞ , y , or Ꭰ Fig . 19 . B OA , & c . , will be null ...
... four points O , A , B , C , by any system of pa- rallel ordinates , into four other A points , o , A , B , C , on any as- sumed plane , the sum of the three projected vectors , a , ẞ , y , or Ꭰ Fig . 19 . B OA , & c . , will be null ...
Page 23
... four complanar points , o , A , B , C , of which no three are collinear , we can ( as in Fig . 18 ) , by what may be ... four dotted lines of Fig . 21 , and twelve other lines , whereof three should be drawn from each of the four given ...
... four complanar points , o , A , B , C , of which no three are collinear , we can ( as in Fig . 18 ) , by what may be ... four dotted lines of Fig . 21 , and twelve other lines , whereof three should be drawn from each of the four given ...
Contents
xxxix | |
xlv | |
lii | |
1 | |
3 | |
7 | |
8 | |
9 | |
12 | |
14 | |
17 | |
21 | |
37 | |
55 | |
60 | |
61 | |
67 | |
83 | |
86 | |
89 | |
92 | |
95 | |
143 | |
206 | |
226 | |
227 | |
263 | |
269 | |
271 | |
289 | |
307 | |
315 | |
321 | |
345 | |
347 | |
354 | |
371 | |
379 | |
387 | |
389 | |
391 | |
411 | |
418 | |
427 | |
435 | |
453 | |
483 | |
495 | |
501 | |
504 | |
569 | |
574 | |
575 | |
581 | |
585 | |
591 | |
593 | |
595 | |
598 | |
601 | |
604 | |
621 | |
629 | |
634 | |
641 | |
642 | |
649 | |
666 | |
669 | |
671 | |
674 | |
676 | |
681 | |
686 | |
689 | |
690 | |
694 | |
700 | |
705 | |
706 | |
709 | |
713 | |
719 | |
726 | |
729 | |
735 | |
736 | |
738 | |
742 | |
757 | |
761 | |
Other editions - View all
Common terms and phrases
ABCD algebra angle anharmonic axis centre CHAP circle coefficients collinear comp Compare the Note complanar cone conic conjugate considered construction curvature curve cyclic deduced denote derived differential diplanar direction ellipsoid equal equation expression formula four fourth proportional function geometrical given plane given points harmonic conjugate imaginary interpreted intersection length line oa linear locus multiplication negative notation osculating osculating circle osculating plane P₁ parallelogram perpendicular positive quadratic quadrilateral quinary radius reciprocal relative direction represented right line right quaternions right quotient right versors roots rotation round scalar SECTION sides sphere spherical spherical angle sub-articles supposed surface symbol tangent tensor ternion theorem tion triangle ABC twisted cubic variable vector VIII whence whereof write