An Elementary Treatise on Algebra: To which are Added Exponential Equations and Logarithms |
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Page 123
... 1 , Nn ( n - 1 ) an - 2 an − 2 N n ( n - 1 ) a " -2 = 2 M 2 nan - 1 n- 1 2 a 186. Corollary . It may be observed , since ( 10b e ) n = 10nben ; so that if , Extraction of Roots . e < CH . IV . § III . ] 123 NUMERICAL EQUATIONS .
... 1 , Nn ( n - 1 ) an - 2 an − 2 N n ( n - 1 ) a " -2 = 2 M 2 nan - 1 n- 1 2 a 186. Corollary . It may be observed , since ( 10b e ) n = 10nben ; so that if , Extraction of Roots . e < CH . IV . § III . ] 123 NUMERICAL EQUATIONS .
Page 124
To which are Added Exponential Equations and Logarithms Benjamin Peirce. so that if , Extraction of Roots . e < 10 , and if 10 % e < 10 % + 1 , ( 103 ... Extraction of Roots . The new approximate root , thus 124 [ CH . IV . § III . ALGEBRA .
To which are Added Exponential Equations and Logarithms Benjamin Peirce. so that if , Extraction of Roots . e < 10 , and if 10 % e < 10 % + 1 , ( 103 ... Extraction of Roots . The new approximate root , thus 124 [ CH . IV . § III . ALGEBRA .
Page 125
To which are Added Exponential Equations and Logarithms Benjamin Peirce. Extraction of Roots . The new approximate root , thus found , is to be used in the same way for a new approximation . The number of places to which each division ...
To which are Added Exponential Equations and Logarithms Benjamin Peirce. Extraction of Roots . The new approximate root , thus found , is to be used in the same way for a new approximation . The number of places to which each division ...
Page 126
... extracting the roots of their numerators and denomi- nators separately . The roots of mixed numbers can be found by reducing them to improper fractions . 188. EXAMPLES . 1. Find the 3d root of 27 . 2. Find the 3d root of 17578 . 3. Find ...
... extracting the roots of their numerators and denomi- nators separately . The roots of mixed numbers can be found by reducing them to improper fractions . 188. EXAMPLES . 1. Find the 3d root of 27 . 2. Find the 3d root of 17578 . 3. Find ...
Page 127
... extraction of the square root . To extract the square root of a number , divide it into periods of two figures each , beginning with the place of units . Find the greatest square contained in the left hand period , and its root is the ...
... extraction of the square root . To extract the square root of a number , divide it into periods of two figures each , beginning with the place of units . Find the greatest square contained in the left hand period , and its root is the ...
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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