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Home > Art, Film & Photography > Essays on the Combinatorial Analysis; Shewing Its Application to Some of the Most Useful and Interesting Problems of Algebra Such as the Expansion of a Multinomial According to Any Given Exponent, the Product of Two or More Multinomials, the Quotie
Essays on the Combinatorial Analysis; Shewing Its Application to Some of the Most Useful and Interesting Problems of Algebra Such as the Expansion of a Multinomial According to Any Given Exponent, the Product of Two or More Multinomials, the Quotie

Essays on the Combinatorial Analysis; Shewing Its Application to Some of the Most Useful and Interesting Problems of Algebra Such as the Expansion of a Multinomial According to Any Given Exponent, the Product of Two or More Multinomials, the Quotie


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About the Book

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. 1818 Excerpt: ... that in all cases the decomposition may be effected by the method of indeterminate problems. The manner of doing this is clearly shewn in pages 29 and 30 of the present Work. While intent upon the solution of a question in which this sort of decomposition was required, the writer of this casually hit upon a method which, though fundamentally the same as that of indeterminate equations, very much diminishes the labour of that process. The principle of this method will be best understood by an example. Suppose we desire to decompose the number 31 from the index-=( 2, 3, 13, 14 Let us first determine the decompositions in which 14 and its multiples can enter. In order to this, take the given number 31; subtract 14, the highest member of the index, and we shall have a principal remainder 31--14--17. Consider this remainder as a number to be decomposed from the index 2, 3, 13 Y, only; treat this new number 17 as before the given number 31; that is, subtract the highest member of this second index, and we shall have 17--13=4. Here it is evident that 4 can only be resolved into 2 + 2, or its equal 12. Hence we obtain this first solution 14+18 + 4 or 14+13 + % the only one in which 14 and 13 can possibly enter at once. Take again the principal remainder 17, and decompose it from the index - 2, 8; that is, subtract successively the higher member of this last index and its multiples as long as we can obtain any positive remainders, and we shall have 17--8=14-v 17--6= 11 # Here the remainders can only be 9--8 further resolved into a and its mul 15_ q tiples, the lowest member of the index; therefore, rejecting the remainders that are odd numbers, we shall obtain the following solutions, still beginning with 14: 14+ 3+14, or 14+ 3 + 72 14+ Q+ 8, or 14 + 33+42 14+1..


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Product Details
  • ISBN-13: 9781231431184
  • Publisher: Rarebooksclub.com
  • Publisher Imprint: Rarebooksclub.com
  • Height: 246 mm
  • No of Pages: 42
  • Spine Width: 2 mm
  • Width: 189 mm
  • ISBN-10: 1231431180
  • Publisher Date: 01 May 2012
  • Binding: Paperback
  • Language: English
  • Returnable: N
  • Weight: 95 gr


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