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Principles of the Algebra of Physics

Principles of the Algebra of Physics


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This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1894 Excerpt: ...a" be another angle, then aAaB = aA+B, so that - and A are truly related as base to index. According to this view the above theorem in plane trigonometry relates to the addition of arcs, but to the product of angles. Let - denote the axis of the constant plane, then (1) takes the form cos aAa" = cos aA+B = cos A cos B--sin A sin B, and (2) takes the form sin aAa" = sin aA+B = cos A sin B + cos B sin A. We may also view A as denoting twice the area of the circular sector, the radius being unity; and this view of the notation is important, for it applies to the equilateral hyperbola, while the former view does not. An angle which is the negative of a given angle has an equal arc, but the opposite axis; (---) is the negative of aA. The minus may. be removed from the base and attached to the index; thus (---)A = aA, and aA--a)B = aAB. So long as the axis remains the same or the opposite, the arcs are combined like ordinary indices. But suppose that a different axis /? is introduced, it is evident that then the rule for indices must be generalized. The V--1 in the ordinary complex quantity denotes an angle whose arc is a quadrant, but it leaves the axis of the plane unspecified. The angle aA is a quaternion with unity for ratio; that is, a versor. The general quaternion may be denoted by a single symbol such as a; and if a denote the ratio, - the axis, and A the arc at unit distance, then a = aaA. Any versor can be expressed as the sum of two quaternions which have arcs differing by a quadrant. Let the arc A be less than a quadrant. Then IT aA = cos A a" 4-sin A a is a complete equivalence. The versor aA applied to any line in its plane leaves the magnitude of the line unchanged, but turns it round a by an amount A. T...


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Product Details
  • ISBN-13: 9781130272369
  • Publisher: Rarebooksclub.com
  • Publisher Imprint: Rarebooksclub.com
  • Height: 246 mm
  • No of Pages: 40
  • Spine Width: 2 mm
  • Width: 189 mm
  • ISBN-10: 1130272362
  • Publisher Date: 01 Mar 2012
  • Binding: Paperback
  • Language: English
  • Returnable: N
  • Weight: 91 gr


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