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

### From inside the book

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**Theorem**. The product of homogeneous polynomials is also homogeneous , and the degree of the product is equal to the sum of the degrees of the factors . Demonstration . For the number of factors in each term of the product is equal to ... Page 22

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**Theorem**. The difference of two integral pos- itive powers of the same degree is divisible by the difference of their roots . Thus , an b " is divisible by a - b . Demonstration . Divide an - br by a - b , as in art . 42 , proceeding ... Page 26

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**Theorem**. The value of a fraction , or of a ratio , is not changed by multiplying or dividing both its terms by the same quantity . Proof . For dividing both these terms by a quantity is the same as striking out a factor common to the ... Page 46

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**Theorem**. The sum of any number of ante- cedents in a continued proportion is to the sum of the corresponding consequents , as one antecedent is to its consequent . Demonstration . Denote the value of each of the ratios in the continued ... Page 49

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**Theorem**. The reciprocals of two quantities are in the inverse ratio of the quantities themselves . Thus A : B = 1 1 : BA 1 1 Demonstration . For A , B , and are four quantities B ' A 1 such that the product of the first A and the last ...### 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