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Elementary Algebra Volume 1-12; With Brief Notices of Its History

Elementary Algebra Volume 1-12; With Brief Notices of Its History


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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. 1879 Excerpt: ...dimensions of B are not higher than those of A. Let A divided by B give a quotient P, with a remainder Cc. Suppose the factor c in Cc not contained in B, let c be rejected and O taken for the second divisor. Next, let B divided by C give a quotient Q, with a remainder Dd. Suppose the factor d in Dd not contained in C, let d be rejected and D taken for the third divisor. Let C divided by B give a quotient R with a remainder 0, then J) will be the highest common divisor of A and B. The process may be thus exhibited, with the following equivalents. B)AP A+BP+Cc, and A-BP= Cc, BP Cc B= CQ+ Dd, B-CQ = Dd, C)B(Q CQ C-DR, C=DR. Dd D)CR PR 0 As an example, find the highest common divisor of 2, + 9jy+Pi/a and Sxi + ixy-lSy. The first term of second quantity cannot he exactly divided by the first term of the first quantity, and in order that it may be divisible, it may be multiplied by the factor 2, which does not enter into every term of the first quantity. 2zJ + 9y+9y')3xa + ixy-Uy 2 W+llxy + Wt, --lSxy--57 /' =--19jf (z + 3, y) The factor--19y iu the remainder may bo rejected, as it forms no factor of tht preceding divisor. i + 3y)2z'+9xy + 9y'(2z + Sy 2x+6xy &ry+9y 3xy+9y Hence x + Zy is highest common divisor of the two expressions. By this method, the highest common divisor of two algebraical polynomials can always be found, when the expressions can be arranged according to the ascending or descending powers of oue of the symbols. In cases, however, where no such arrangement is possible, the common factors may in general be found by inspection. First, every divisor of A and B divides BP, a multiple of B, and therefore it divides A--BP or Cc, and therefore also C. And every divisor of A and B divides C, and therefore B--CQ or Dd, and therefore D. Hence e...


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Product Details
  • ISBN-13: 9781159885458
  • Publisher: Rarebooksclub.com
  • Publisher Imprint: Rarebooksclub.com
  • Height: 246 mm
  • No of Pages: 146
  • Spine Width: 8 mm
  • Width: 189 mm
  • ISBN-10: 1159885451
  • Publisher Date: 01 May 2012
  • Binding: Paperback
  • Language: English
  • Returnable: N
  • Weight: 272 gr


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