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Elements of Algebra Priliminary to the Differential Calculus

Elements of Algebra Priliminary to the Differential Calculus


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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. 1837 Excerpt: ...and write 1 in its place; or, 2. Let x (which as yet has no meaning) stand for 1; in which case the rule does apply, and gives the true result. Therefore, we lay down the following definition. By any letter with the exponent 0, such as a," we mean 1; or every quantity raised to the power whose exponent is 0, is 1. Anomaly 2. If we apply the equation xa--xb = -6 to a case in which b is greater than a, say b = a-f-6, the mere rule gives of H-x+6 = afia+6) = x6 a result which has no meaning. The reason is as before; a rule has been applied to a case to which it was not meant to apply. To find the rational result, remember that xa+e = x x x6; and x" x" 1 xa+6 I'xi x6 the last result being obtained by dividing both numerator and denominator of the preceding fraction by x." The following are similar instances; in the first column is the rational process, in the second the (yet) improper extension of the rule: To make the rale applicable, we must agree that (which as yet have no meaning) shall stand for? 7 and? thai is, instead of x-1 being the sign that the result is to be abandoned, and t--x written in its place, we agree that xl shall mean the same as 1-i-x. And we are at liberty to give J--1 any meaning we please, because as yet it is without meaning. We lay down, therefore, the following definition: A letter with a negative exponent means unity divided by the tame letter with the tame numerical exponent taken positively; or, . 1 X means--x Our two rules for multiplication and division will now be found to be universal. The following are instances, arranged as before: i-, . J--_J--_ S.13' x xX x3 X x3 x3--X3 x Jr--x3x xx3+ xi We have now added to our first definition of an exponent in such a way that two fundamental rules remain true iu...


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Product Details
  • ISBN-13: 9781130143881
  • Publisher: Rarebooksclub.com
  • Publisher Imprint: Rarebooksclub.com
  • Height: 246 mm
  • No of Pages: 66
  • Spine Width: 4 mm
  • Width: 189 mm
  • ISBN-10: 1130143880
  • Publisher Date: 01 Mar 2012
  • Binding: Paperback
  • Language: English
  • Returnable: N
  • Weight: 136 gr


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