An Elementary Treatise on Algebra: To which are Added Exponential Equations and Logarithms |
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Page 24
... successively obtained by dividing the coefficient a2 - b2 of 23 in the dividend , the coefficient a2 - 2 a b + b2 of x2 in the first remainder , and the coefficient a2 + 2 ab 62 of x in the second re- - mainder , by the coefficient a ...
... successively obtained by dividing the coefficient a2 - b2 of 23 in the dividend , the coefficient a2 - 2 a b + b2 of x2 in the first remainder , and the coefficient a2 + 2 ab 62 of x in the second re- - mainder , by the coefficient a ...
Page 30
... successive divisions , that the term of the dividend , from which the term of the quotient is to be obtained , is not divisible by the corre- sponding term of the divisor . This , sometimes , arises from a monomial factor of the divisor ...
... successive divisions , that the term of the dividend , from which the term of the quotient is to be obtained , is not divisible by the corre- sponding term of the divisor . This , sometimes , arises from a monomial factor of the divisor ...
Page 72
... successive hour , 55 minutes later . 31. Two bodies move after one another in the circum- ference of a circle , which measures p feet . At first they are distant from each other by an arc measuring a feet ; the first moves c feet , the ...
... successive hour , 55 minutes later . 31. Two bodies move after one another in the circum- ference of a circle , which measures p feet . At first they are distant from each other by an arc measuring a feet ; the first moves c feet , the ...
Page 102
... successive remainder may be placed equal to zero . But a remainder will at last be obtained , which does not contain the quan- tity to be eliminated ; and the equation , formed from placing this remainder equal to zero , is the equation ...
... successive remainder may be placed equal to zero . But a remainder will at last be obtained , which does not contain the quan- tity to be eliminated ; and the equation , formed from placing this remainder equal to zero , is the equation ...
Page 121
... successive values of m above each horizontal line with those of h m below it . In the second column are placed the successive values of the divisor M. In the third column the first approximation a is placed at the top of the table , -m ...
... successive values of m above each horizontal line with those of h m below it . In the second column are placed the successive values of the divisor M. In the third column the first approximation a is placed at the top of the table , -m ...
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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