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

### From inside the book

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**suppressing**in the dividend all the factors of the divisor which are ex- plicitly contained in the dividend , and simply indicating the division with regard to the remaining factors of the divisor . Hence , from art . 28 ,**Suppress**the ... Page 30

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**suppressed**. For , since the greatest common divisor of two quantities is only the product of their common factors , it is not affected by any factor of the one quantity which is prime to the other . Hence any monomial factor of either ... Page 31

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**suppressed**at first , and afterwards multiplied by the greatest common divisor of the re- maining polynomials . Since any quantity which is divisible by A is also divis- ible by - · A ; and any quantity which is divisible by - A is also ... Page 32

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**suppression**of the factor a , is the 4th line of col . 2 , and is used to divide the 1st line of col . 1. The 2d line of col . 1 is the 1st line multiplied by 7 in order to render its first term divisible by the first term of the new ... Page 33

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**suppress**it , and they become 3 a x7 3 a2 x6 24 a5 x3 . 2 b2 c x4-2 a b2 c x3 + 4 a2 b2 c x2-6 a3 b2 c x - 20 a1 b2 c . The greatest common divisor of these two quantities , found as in the preceding example , is x - 2 a , which , mul ...### Other editions - View all

### Common terms and phrases

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