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

### From inside the book

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**unity**. Thus , in the expression 15 ab , 15 is the numerical co- efficient of a b ; and , in the expression xy , 1 may be re- garded as the coefficient of xy . 6. The continued product of a quantity multiplied repeatedly by itself , is ... Page 3

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**unity**. Thus the fifth power of a is written as ; but when a stands by itself , it may be regarded as a1 . 7. The root of a quantity is the quantity which , multiplied a certain number of times by itself , pro- duces the given quantity ... Page 14

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**unity**, the quotient is simply equal to the remaining portion of the dividend . The sign of the quotient must , from art . 30 , be the same as that of the divisor when the dividend is positive , and it must be the reverse of that of the ... Page 16

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**unity**. Whence any quantity with an exponent equal to zero is**unity**. Thus , amam 1 . 36 38. 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 ... Page 23

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**unity**and increasing that of b by**unity**; and the number of terms is equal to the exponent n . 51. Corollary . If b is put equal to a in the preceding quotient , each of its terms becomes equal to an - 1 , which gives the peculiar ...### 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