An Elementary Treatise on Algebra: To which are Added Exponential Equations and Logarithms |
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Page 118
... approximate value of x , we have m a = a M ' which may be used in the same way in which a was , in order to find a new approximate value a " of x ; and if m ' and M ' denote the corresponding values of u and U , we shall have m ' a ...
... approximate value of x , we have m a = a M ' which may be used in the same way in which a was , in order to find a new approximate value a " of x ; and if m ' and M ' denote the corresponding values of u and U , we shall have m ' a ...
Page 249
... value of the continued fraction 1 1 2+ 1 3+ 4 2. Find the value of the continued fraction Ans . 18 . 1 1 4+ 3 + 2 Ans . J. Approximate Values of Continued Fractions . 319. Problem . continued CH . IX . ] 249 CONTINUED FRACTIONS .
... value of the continued fraction 1 1 2+ 1 3+ 4 2. Find the value of the continued fraction Ans . 18 . 1 1 4+ 3 + 2 Ans . J. Approximate Values of Continued Fractions . 319. Problem . continued CH . IX . ] 249 CONTINUED FRACTIONS .
Page 250
To which are Added Exponential Equations and Logarithms Benjamin Peirce. Approximate Values of Continued Fractions . 319. Problem . continued fraction . To find the value of an infinite Solution . Let the fraction be 1 1 a + b + c + & c ...
To which are Added Exponential Equations and Logarithms Benjamin Peirce. Approximate Values of Continued Fractions . 319. Problem . continued fraction . To find the value of an infinite Solution . Let the fraction be 1 1 a + b + c + & c ...
Page 251
... approximate values , the 1 ) st , and the ( n — 2 ) nd , by multiplying the ( n ( n - - 1 ) st numerator by the nth denominator con- tained in the given continued fraction , and adding to the result the numerator of the ( n proximate value ...
... approximate values , the 1 ) st , and the ( n — 2 ) nd , by multiplying the ( n ( n - - 1 ) st numerator by the nth denominator con- tained in the given continued fraction , and adding to the result the numerator of the ( n proximate value ...
Page 252
... approximate value , it follows that it must be true for every succeeding value . But the comparison of the values given in the preceding article shows that it is true for the third value , and therefore for every succeeding value . 321 ...
... approximate value , it follows that it must be true for every succeeding value . But the comparison of the values given in the preceding article shows that it is true for the third value , and therefore for every succeeding value . 321 ...
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126 become zero 3d root arithmetical progression coefficient commensurable roots common difference contained continued fraction continued product Corollary deficient terms denote derivative Divide dividend division equal roots equal to zero equation x² factor Find the 3d Find the 4th Find the continued Find the greatest Find the number Find the square Find the sum Free the equation Geometrical Progression given equation given number gives greatest common divisor Hence imaginary roots last term least common multiple letter logarithm monomials multiplied number of real number of terms polynomial positive roots preceding article Problem quantities in example quotient radical quantities ratio real roots reduced remainder required equation required number row of signs Scholium Second Degree Solution Solve the equation square root Sturm's Theorem subtracted Theorem unity unknown quan unknown quantity variable whence