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" Divide the first term of the remainder by twice the first term of the root, and add the quotient to the part of the root already found, and also to the trial-divisor. "
Elementary Algebra - Page 211
by John Henry Tanner - 1904 - 364 pages
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Elements of Algebra

William Smyth - Algebra - 1830 - 278 pages
...remainder therefore by twice the terms of the root already found, or which is the same thing, dividing the first term of the remainder by twice the first term of the root, we shall obtain the third term sought. Subtracting from the first remainder twice the product of the...
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A Practical System of Algebra: Designed for the Use of Schools and Private ...

Peter Nicholson - Algebra - 1831 - 326 pages
...this : Find the root of the first term, and subtract it therefrom, then bring down the next two terms, and divide the first term of the remainder by twice the first term of the root, and put the result both in the quotient and divisor ; then proceed as in arithmetic. EXAMPLES. (')...
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A Catechism and Notes Upon the Algebras of Bourbon and Lacroix: For the Use ...

Charles William Hackley - Algebra - 1834 - 38 pages
...third term of the root ; raise the three terms of the root found to the «"1 power, which subtract from the given polynomial and divide the first term of the remainder by n times the n — 1 power of the first term of the root, and the quotient will be the fourth term of...
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The Elements of Algebra: Designed for the Use of Students in the University

John Hind - Algebra - 1837 - 584 pages
...be obtained: but 2ab + b2 is the same as (2 a + b) b, and therefore b will be determined by dividing the first term of the remainder by twice the first term of the root, and to complete the operation, twice this first term THE SQUARE EOOT. together with the second must...
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An Elementary Treatise on Algebra: To which are Added Exponential Equations ...

Benjamin Peirce - Algebra - 1837 - 300 pages
...Double the part of the root thus found for a divisor, subtract the square of this part of the root from the given polynomial, and divide the first term of the remainder by the divisor ; the quotient is the second term of the root. Double the terms of the root already found...
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An Elementary Treatise on Algebra: To which are Added Exponential Equations ...

Benjamin Peirce - Algebra - 1837 - 302 pages
...Double the part of the root thus found for a divisor, subtract the» square of this part of the root from the given polynomial, and divide the first term of the remainder by the divisor ; the quotient is the second term of the root. Double the terms of the root already found...
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The principles of arithmetic. [Followed by] The principles of algebra

Wales Christopher Hotson - 1842 - 306 pages
...is a, the first term of the root; subtracting its square from the whole quantity and dividing 2a6, the first term of the remainder, by twice the first term of the root, we obtain b, the second term of the root ; adding b to 2a, proceeding with 2a + b as a divisor and...
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Elements of Algebra: Including Sturms' Theorem

Charles Davies - Algebra - 1845 - 382 pages
...will give the first term of the root. Subtract the square of this term from the given polynomial. II. Divide the first term of the remainder by twice the first term of the root, and the quotient will be the second term of the root. III. From the first remainder subtract the product...
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An Elementary Course of Mathematics: Designed Principally for Students of ...

Harvey Goodwin - Mathematics - 1846 - 500 pages
...term of the root. By precisely similar reasoning it will appear, that if we subtract (a + bx + ea?)" from the given polynomial and divide the first term of the remainder by na"-1, we shall obtain the fourth term of the root ; and so on. EXAMPLE. Extract the fourth root of...
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The elements of algebra, with additions by W. Galbraith and W. Rutherford

John Bonnycastle - 1848 - 334 pages
...first term of the root, and subtract the corresponding power of this term from the given quantity ; divide the first term of the remainder by twice the first term of the root, for the square root ; by three times the square of the first term of the root, for the cube root, and...
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