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Home > History and Archaeology > History > Elements of Algebra, Compiled from Garnier's French Translation of L. Euler. to Which Are Added, Solutions of Several Miscellaneous Problems
Elements of Algebra, Compiled from Garnier's French Translation of L. Euler. to Which Are Added, Solutions of Several Miscellaneous Problems

Elements of Algebra, Compiled from Garnier's French Translation of L. Euler. to Which Are Added, Solutions of Several Miscellaneous Problems


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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. 1824 Excerpt: ...power, either of a + b, or a--b. We must remark, first, that if we can find any power of a + b, we can immediately discover the same power of a--b, since it will be necessary only to change the signs of the even terms, that is to say, of the 2d, 4th, 6th, &c. We have therefore only to establish a rule by which any power of a+b may be found, without going through the ordinary method of multiplication in the preceding powers. 258. Now 258. Now we may observe, that if we take away from the powers which we have already determined, the letters or coefficients which precede each term, we shall perceive in all the terms this singular order. First, we shall see the first term a of the root raised to the power required; and that in the succeeding terms the powers of a diminish continually by unity, while the powers of b are increased in the same manner; so that the sum of the exponents or indices of a and b is always the same, and equal to the exponent of the power required, and, that at the end is found the term b by itself raised to the same power. So that if the tenth power of a + b were required, we should at least be certain of this, that the order of the terms, without their coefficients, would succeed each other in the following series, a,0+a6 + a9b + a'b3 + aBbt + ahbh + ab6 + a3V + aW + ab + b10. 259. It remains therefore to show how we may determine the coefficients which belong to each term, or, in other words, the numbers by which those terms are to be multiplied. Now with respect to the first term, its coefficient is always unity; and with respect to the second, the coefficient is always the same with the exponent of the power. With regard to the other terms it is not so easy to discover the order of their coefficients; but by continuing them, we sh...


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Product Details
  • ISBN-13: 9781130873580
  • Publisher: Rarebooksclub.com
  • Publisher Imprint: Rarebooksclub.com
  • Height: 246 mm
  • No of Pages: 58
  • Spine Width: 3 mm
  • Width: 189 mm
  • ISBN-10: 1130873587
  • Publisher Date: 01 Mar 2012
  • Binding: Paperback
  • Language: English
  • Returnable: N
  • Weight: 122 gr

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Elements of Algebra, Compiled from Garnier's French Translation of L. Euler. to Which Are Added, Solutions of Several Miscellaneous Problems
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