 X r' • 6< = rr' -0 + 0'; in words, the length of the product is the product of the lengths, and the angle of the product is the sum of the angles. Now the principle of the permanence of equivalent forms does not help us to generalize this proposition...  Proceedings - Page 35by American Association for the Advancement of Science - 1892Full view - About this book
 | American Association for the Advancement of Science - 1892 - 510 pages
...0 with an initial line in a given pliine. For this generalized magnitude r-0X r'-0'=rr' • 8 + 6'; In words, the length of the product Is the product...hypothesis likely to present itself at first Is : Let y denote the angle between the given plane and a fixed plane, is (r • 0 • ?>) X (r> • 6' •... | |
 | American Association for the Advancement of Science - 1892 - 516 pages
...to have any angle 0 with an initial line in a given plane. For this generalized magnitude fflX r'-0' =rr' • 0 + 0'; in words, the length of the product is the prod uct of the lengths, and the angle of the product is the sum of the angles. Now the principle of... | |
 | American Association for the Advancement of Science - 1892 - 516 pages
...initial line in a given plane. For this generalized magnitude r • e X r' • d> = rr> • 0 + 8' ; in words, the length of the product is the product...between the given plane and a fixed plane, is (r • 0 • <f ) X (r' • (/' • <p') = TT< • 0 + 0' • <f + y>'? This is a question not of symbolism,... | |
 | American Association for the Advancement of Science - 1892 - 512 pages
...so as to have any angle 0 with an initial line in a given plane. For this generalized magnitnde r- 0 X r'- 6' =rr' -0 + 0'; in words, the length of the...hypothesis likely to present itself at first is : Let y' denote the angle between the given plane and a fixed plane, is (r • 0 • yO X (r' • 0' •... | |
 | American Association for the Advancement of Science - 1892 - 510 pages
...0 with an initial line in a given plane. For this generalized magnitude r-0 X r1' 01 =n-' • е + 0'; in words, the length of the product is the product...hypothesis likely to present itself at first is : Let n,- denote the angle between the given plane and a fixed plane, is (r • 0 • ci) X (r' • 0' •... | |
 | Alexander Macfarlane - 1894 - 244 pages
...have any angle 0 with an initial line in a given plane. For this generalized magnitude r- 6 X r'' 0' =rr' • 0 + 0'; in words, the length of the product...the angle of the product is the sum of the angles. Kow the principle of the permanence of equivalent forms does not help us to generalize this proposition... | |
 | American Association for the Advancement of Science - 1892 - 506 pages
...angle 0 with an Initial line in a given plnne. For this generalized magnitude r • 6 X r' • 0' = rr' • 0 + 0'; in words, the length of the product...angle between the given plane and a fixed plane, is (•• • 6 • p) X (r> • 0' • p') =rr' • 6 + 0' • <f + y'? This is a question not of symbolism,... | |
 | J. B. Kuipers - 1999 - 398 pages
...turns out that the magnitude of the product is equal to the product of the magnitudes of the factors, and the angle of the product is the sum of the angles of the two factors. This fact is apparent if we represent the complex number in trigonometric form.... | |
 | Ira Ritow - 2003 - 216 pages
...easily. The magnitude of their product is the product of the individual magnitudes of the multipliers and the angle of the product is the sum of the angles of the multipliers. That is, X Beb} = This is illustrated in Fig. 50. :C.Ax8 Sum of angles Product... | |
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