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

### From inside the book

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**preceding article**is called an arrangement according to the descending powers of the letter . 45. Corollary . Negative powers are considered to be lower than positive powers , or than the power zero , and the larger the absolute value ... Page 28

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**preceding article**, divisible by the greatest common divisor . In the same way , from this remainder and the divisor a still smaller remainder can be found , which is divisible by the greatest common divisor ; and , by continuing this ... Page 29

... preceding di- visor is exactly divisible by it without any remainder . The quantity thus obtained , must be the greatest common divisor required ; for , from the

... preceding di- visor is exactly divisible by it without any remainder . The quantity thus obtained , must be the greatest common divisor required ; for , from the

**preceding article**, the great- est common divisor of each remainder and ... Page 36

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**preceding article**, be reduced to an equivalent frac- tional expression having any required denominator , by regarding it as a fraction , the denominator of which is unity . 70. EXAMPLES . 1. Reduce 325 8 ' 3 ' 6 ' to the common ... Page 46

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**preceding article**by M , and we have MA : B = = C : D E : F , & c .; whence A = BX M C = D × M E = F × M , & c .; and the sum of these equations is A + C + E + & c . = ( B + D + F + & c . ) x M ; Ratio of Sum of Antecedents to Sum of ...### 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