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Hirsch's Collection of Examples, Formulaee, & Calculations, on the Literal Calculus and Algebra

Hirsch's Collection of Examples, Formulaee, & Calculations, on the Literal Calculus and Algebra


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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. 1827 Excerpt: ...or A, = A, gives in the preceding, are called recurring transpositions, and the periods which are obtained from them, recurring periods. The characteristic feature of transpositions of this kind consists in this, that each root is removed one place forwards or backwards, and in the first case the last takes the place of the first; but in the second case, the first takes the place of the last, so that there is a kind of circular motion; as if, for instance, a number of persons stand in a circle, having their backs to each other, and all walking at the same time either backwards or forwards. The transpositions are called recurring ones, when only some of the roots move in the manner just mentioned, but the remaining ones retain their places. Thus the equation /: (12345678) = /: (34512678) only gives recurring transpositions of the first five roots. The law of the preceding is also true for this, when we take for n merely the number of the roots to be transposed, and the remaining ones are considered, as though they did not exist. SECTION CLV. Rule. If the equation x" + A.x"'1 + Bx"-+ &c. = o, by the introduction of a function t=f: (12345...-), be transformed into an equation of two terms f--K = o: then the roots of this last equation t', t," t'," tw are always the numerical values of such values of forms of the function t, as, taken together, form a period. Proof. The roots of the equation t"--K = o may always, as may be seen from the fifth chapter, be expressed by t', at', aH', aH', a"l t', when a denotes a primitive root of the equation f--1 =o. Therefore " = at', t'" = at," t/r = at'," ( = at'-l t' = atw. Now, let A A.a A3, At, A denote the values of forms, which co...


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Product Details
  • ISBN-13: 9781130509946
  • Publisher: Rarebooksclub.com
  • Publisher Imprint: Rarebooksclub.com
  • Height: 246 mm
  • No of Pages: 88
  • Spine Width: 5 mm
  • Width: 189 mm
  • ISBN-10: 113050994X
  • Publisher Date: 01 Mar 2012
  • Binding: Paperback
  • Language: English
  • Returnable: N
  • Weight: 172 gr


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