An Elementary Treatise on Algebra: To which are Added Exponential Equations and Logarithms |
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Page 22
... integral pos- itive powers of the same degree is divisible by the difference of their roots . Thus , an - bn is divisible by a- - - b . 18 Demonstration . Divide an - bn by a— - b , as in art . 42 , proceeding only to the first ...
... integral pos- itive powers of the same degree is divisible by the difference of their roots . Thus , an - bn is divisible by a- - - b . 18 Demonstration . Divide an - bn by a— - b , as in art . 42 , proceeding only to the first ...
Page 124
... integral power contained in the left hand period ; and the root of this power is the left hand figure of the required root , and is just as many places distant from the decimal point as the corresponding period is removed by periods ...
... integral power contained in the left hand period ; and the root of this power is the left hand figure of the required root , and is just as many places distant from the decimal point as the corresponding period is removed by periods ...
Page 141
... integral powers of x are written in the second member , because the product could , evidently , give no others , and all the positive integral powers of x are included , because the coefficients of any which are super- fluous must be ...
... integral powers of x are written in the second member , because the product could , evidently , give no others , and all the positive integral powers of x are included , because the coefficients of any which are super- fluous must be ...
Page 173
... integral or frac- tional . 235. EXAMPLES . 1. Solve the equation A x2n + B x2 + M = 0 . Solution . If the square is completed , as in the preceding article , and the square root extracted , the result is Ax + B = ± √ ( AM + B2 ) ...
... integral or frac- tional . 235. EXAMPLES . 1. Solve the equation A x2n + B x2 + M = 0 . Solution . If the square is completed , as in the preceding article , and the square root extracted , the result is Ax + B = ± √ ( AM + B2 ) ...
Page 240
... = 1 is when x - 1 it is + , + , + + ; - + - + - + -- + 一, + , - , - , + , - , + ; so that the number of these roots cannot exceed 8 . Integral Root . Again , when x is infinitely little 240 [ CH . VIII . § III . ALGEBRA .
... = 1 is when x - 1 it is + , + , + + ; - + - + - + -- + 一, + , - , - , + , - , + ; so that the number of these roots cannot exceed 8 . Integral Root . Again , when x is infinitely little 240 [ CH . VIII . § III . ALGEBRA .
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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