An Elementary Treatise on Algebra: To which are Added Exponential Equations and Logarithms |
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Page 22
... true for any power , as the ( n − 1 ) st , it also holds for the nth , or the next greater . But from examples , 10 , 11 , 12 , 13 of art . 43 , the propo- sition holds for the 2d , 3d , 4th , and 5th ; and therefore it must be true ...
... true for any power , as the ( n − 1 ) st , it also holds for the nth , or the next greater . But from examples , 10 , 11 , 12 , 13 of art . 43 , the propo- sition holds for the 2d , 3d , 4th , and 5th ; and therefore it must be true ...
Page 75
... true solution ; and sometimes it indicates an impossibility in the proposed question . In any such case , therefore , it is necessary to return to the data of the problem and investigate the signification of this result . 128. EXAMPLES ...
... true solution ; and sometimes it indicates an impossibility in the proposed question . In any such case , therefore , it is necessary to return to the data of the problem and investigate the signification of this result . 128. EXAMPLES ...
Page 76
... true solution . 4. In what cases would the value of one of the unknown quantities in example 39 of art . 126 become zero ? and what would this value signify ? Ans . When b = na , or = ma ; 1 and these equations indicate that a is itself ...
... true solution . 4. In what cases would the value of one of the unknown quantities in example 39 of art . 126 become zero ? and what would this value signify ? Ans . When b = na , or = ma ; 1 and these equations indicate that a is itself ...
Page 81
... true solution of the problem ; and if the solution gives no other than negative values for this quantity , the problem is generally impossible . But , in this case , the negative of the negative value of the unknown quantity is positive ...
... true solution of the problem ; and if the solution gives no other than negative values for this quantity , the problem is generally impossible . But , in this case , the negative of the negative value of the unknown quantity is positive ...
Page 83
... true solutions . 5. In what cases would the values of either of the un- known quantities in example 38 of art . 126 be negative ? why should this be the case ? and could the enunciation be corrected for this case ? Ans . If we suppose ...
... true solutions . 5. In what cases would the values of either of the un- known quantities in example 38 of art . 126 be negative ? why should this be the case ? and could the enunciation be corrected for this case ? Ans . If we suppose ...
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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