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

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... so as to make it -A + B .

... so as to make it -A + B .

**Hence**, To subtract one quantity from another , change the signs of the quantity to be subtracted from + to - , Multiplication of Monomials . and from - to + , 8 [ CH . I. § III . ALGEBRA . III Subtraction. Page 10

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**Hence**the coefficient of the product of given mono- mials is the product of their coefficients . The different powers of the same letter may also be brought together , and since , by art . 6 , each exponent de- notes the number of times ... Page 11

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**Hence**, The product of two polynomials is obtained by multiplying each term of one factor by each term of the other , as in art . 28 , and the product of two terms which have the same sign is to be affected with the sign + , while the ... Page 14

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**Hence**, from art . 28 , Suppress the greatest common factor of the nu- merical coefficients . Suppress each letter of the divisor or dividend in the term in which it has the least exponent , and re- tain it in the other term , giving it ... Page 29

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**hence**, it is the same with that of any divisor and its dividend , or with that of the given quantities . 61. Corollary . When the remainders decrease to unity , the given quantities have no common divisor , and are said to be ...### 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