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

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Page 119

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**decimals**, as the gth , this will be shown by the magnitude of e , for we shall find 1 . e < 108 and , consequently , 1 e2 < 102 g ' Rate of Approximation . N If also the value of CH . IV . § III . ] 119 NUMERICAL EQUATIONS . Page 120

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**decimals**and the division of m by M may be carried to this extent . 182. Corollary . the form When the given equation has u = h , in which h is a given number , it may be brought to the form u - · h = 0 , so that the value of the final ... Page 121

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**decimals**. - This process may be arranged in the following form , in the first column of which , h is placed at the top , and the successive values of m above each horizontal line with those of h m below it . In the second column are ... Page 124

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**decimal**point , that of the power must be as many as b times n places from this point , and less than b + 1 times n places from it ; which , combined with the preceding articles , gives the following rule for finding , the root of a ... Page 128

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**decimals**by first reducing them to**decimals**. The Square Root of Numbers . 192. EXAMPLES . 1. 128 [ CH . IV . § III . ALGEBRA .### 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