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A Practical System of Algebra; Designed for the Use of Schools and Private Students

A Practical System of Algebra; Designed for the Use of Schools and Private Students


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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. 1831 Excerpt: ...is equal to the sum of the next coefficient above it, and the product of the next coefficient on the left (of the above coefficient), and the quantity e. This general relation may be expressed as follows; let Q and R be two coefficients in any two consecutive terms whatever, of the original equation, which we shall suppose to be of the rath degree, then the value of the coefficient of the transformed equation of the same number as R will be Bn=eQn-i+Bnlt observing, however, that if Q be the coefficient of the first term of the original equation, we must substitute A for Q _ t; and if Q be the last term but one, or of the same number, as the degree of the equation, we must substitute the last coefficient, or absolute number, of the original equation, instead of the coefficient, Rn_ a, of the next preceding transformed equation. In conformity to these two observations, suppose the original equation to be a cubic, then will -=3, and n--1=2. Suppose, again, Q and R to be the coefficients of the first and second terms of the original equation, then Q and 72 will become A and B; hence, in the transformed equation, i? =e(? --J+/in--i will become B, = eA--B1; and if Q and R be the coefficients of the second and third terms of the original equation, then Q and R will become B and C; hence, in the transformed equation 7?-=e?n-i+.Hn-i will become C3=cB3+C2; moreover, if Q and R be the coefficients of the third and fourth terms of the original cubic, Q and R will become C and D; hence, in the transformed equation i?-=eQ--i+/fm-i will become D3=eC2--D. These values will be found to agree with the tabulated values before exhibited; hence, in a transformed quadratic, we cannot have C, nor in a cubic D3, nor in a biquadratic ...


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Product Details
  • ISBN-13: 9781130060386
  • Publisher: Rarebooksclub.com
  • Publisher Imprint: Rarebooksclub.com
  • Height: 246 mm
  • No of Pages: 38
  • Spine Width: 2 mm
  • Width: 189 mm
  • ISBN-10: 1130060381
  • Publisher Date: 01 Mar 2012
  • Binding: Paperback
  • Language: English
  • Returnable: N
  • Weight: 86 gr


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