## An Elementary Treatise on Algebra: To which are Added Exponential Equations and Logarithms |

### From inside the book

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**give**+ ; unlike signs**give**- . 36. EXAMPLES . 13 b 1. Divide 65 ab by 5 a . Ans . 13 b . 1 2. Divide - 132 a5 63 c by 11 a3 63 . Ans . -12 a2 с . 3. Divide 144 a 63 c2 d8 e by - 112 a b c e7 h . 9 c d8 Ans . 7 beh 27 4. Divide - 135 by ... Page 23

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**gives**the peculiar result an an a a nan - 1 52. There are sometimes two or more terms in the divisor , or in the dividend , or in both , which contain the same highest power of the letter accord- ing to which the terms are arranged . In ... Page 31

... all the terms of the first of them , and the factor x common to all the terms of the second , being suppressed in columns 1 and Greatest Common Divisor . 2 ,

... all the terms of the first of them , and the factor x common to all the terms of the second , being suppressed in columns 1 and Greatest Common Divisor . 2 ,

**give**the first lines CH . II . § 1. ] 31 REDUCTION OF FRACTIONS . Page 32

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**give**the first lines of the following form of the process , which is similar to that in art . 62 . Col. 1 . 2 x3 +7 α x2- 9 аз 14 x3 + 49 a x2 - 63 a3 | 14 x3 - 5 a x2 - 39 a2 x 54 a x2 +39 a2 x - 63 a3 18 x2 + 13 a x - 21 a2 126 x2 +91 ... Page 33

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**gives**7 a2 b ( x - 2 a ) for the required greatest common divisor . 3. Find the greatest common divisor of 23 Ans . x a3 and - а . 4. Find the greatest common divisor of 5 a3- 10 a2b + Ans . a + b . 15 63 and 3 a3 + 6a2b + 6ab2 + 363 ...### Other editions - View all

### Common terms and phrases

126 become zero 3d root arithmetical mean arithmetical progression Binomial Theorem 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 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