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

### From inside the book

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**Corollary**. The continued product of several monomials is , as in examples 8 and 9 , positive , when the number of negative factors is even ; and it is negative , as in example 10 , when the number of negative factors is odd . 33.**Corollary**... Page 15

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**Corollary**. If the rule for the exponents is applied to the case in which the exponent of a letter in the dividend is equal to its exponent in the divisor , when , for instance , am is to be divided by am , the exponent of the letter in ... Page 16

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**Corollary**. When , in example 6 of art . 30 , the ex- ponent n of a in the divisor is greater than its exponent m in the dividend , the exponent m - n in the quotient is nega- tive ; and a negative exponent is thus substituted for the ... Page 20

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**Corollary**. The quotient can be obtained with equal facility by using the terms which contain the lowest powers of a letter instead of those which con- tain the highest powers . In this case , it is more convenient to place the term ... Page 22

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**Corollary**. The division of an continued for the purpose of showing the form of the quotient , a . - -bn an ・ an - a ∙ 1b an an - 1b an - 1b - b qn − 1 + an − 2 b + an - 3b2 + & c ..... + abn − 2 + bn − 1 bn an − 2 b2 an - 2 b2bn ...### 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