Dynamics. Vector Analysis and Multiple Algebra. Electromagnetic Theory of Light, Etc

Dynamics. Vector Analysis and Multiple Algebra. Electromagnetic Theory of Light, Etc

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This historic book may have numerous typos and missing text. Purchasers can usually download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1906 edition. Excerpt: ...cases will be found in which the quaternionic idea forms an essential element in the signification of the equations. The question will then arise with respect to the comparatively limited field which is the peculiar property of Hamilton, How im portant are the advantages to be gained by the use of the quaternion? This question, unlike the preceding, is one into which a personal equation will necessarily enter. Everyone will naturally prefer the methods with which he is most familiar; but I think that it may be safely affirmed that in the majority of cases in this field the advantage derived from the use of the quatemion is either doubtful or very trifling. There remains a residuum of cases in which a substantial advantage is gained by the use of the quaternionic method. Such cases, however, so far as my own observation and experience extend, are very exceptional. If a more extended and careful inquiry should show that they are ten times as numerous as I have found them, they would still be exceptional. We have now to inquire what we find in the Au, sdehn'um, .slehre in the way of a geometrical algebra, that is wanting in quaternions. In addition to an algebra of vectors, the Ausdehnungslehre affords a system of geometrical algebra in which the point is the fundamental element, and which for convenience I shall call Grassmann's algebra of points. In this algebra we have first the addition of points, or quantities located at points, which may be explained as follows. The in which the capitals denote points, and the small letters scalars (or ordinary algebraic quantities), signifies that and also that the centre of gravity of the weights a, b, c, etc., at the points A, B, C, etc., is the same as that of the weights e, f, etc., at the...show more

Product details

  • Paperback | 96 pages
  • 189 x 246 x 5mm | 186g
  • Rarebooksclub.com
  • United States
  • English
  • black & white illustrations
  • 1236786831
  • 9781236786838