An Elementary Treatise on Algebra: To which are Added Exponential Equations and Logarithms |
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Page 53
... from the second orifice with a velocity ths of that which it should have to discharge 13 x in the given time , its actual discharge must be 7 ( 13x ) = = f f x ; whence the required equation is ZJ x x = 561 . 8. A dog pursues a hare ...
... from the second orifice with a velocity ths of that which it should have to discharge 13 x in the given time , its actual discharge must be 7 ( 13x ) = = f f x ; whence the required equation is ZJ x x = 561 . 8. A dog pursues a hare ...
Page 63
... from negative Exponents . 115. Corollary . If the given equation contains negative exponents , it can be freed from them by arts . 80 and 82 . 116. EXAMPLES . 1. Free the equation x + x - 1 x -X = 2-1 from fractions and negative ...
... from negative Exponents . 115. Corollary . If the given equation contains negative exponents , it can be freed from them by arts . 80 and 82 . 116. EXAMPLES . 1. Free the equation x + x - 1 x -X = 2-1 from fractions and negative ...
Page 65
To which are Added Exponential Equations and Logarithms Benjamin Peirce. Equations ... equation of the first degree with one unknown quantity is reduced , as in ... given equation to the form Ax + B = 0 , transpose B to the second member by ...
To which are Added Exponential Equations and Logarithms Benjamin Peirce. Equations ... equation of the first degree with one unknown quantity is reduced , as in ... given equation to the form Ax + B = 0 , transpose B to the second member by ...
Page 66
To which are Added Exponential Equations and Logarithms Benjamin Peirce. Cases in Equations in the First Degree . Hence ... given equation is , however , in this case , 0x x + B = 0 , Cases in Equations of the First Degree . which reduces ...
To which are Added Exponential Equations and Logarithms Benjamin Peirce. Cases in Equations in the First Degree . Hence ... given equation is , however , in this case , 0x x + B = 0 , Cases in Equations of the First Degree . which reduces ...
Page 67
To which are Added Exponential Equations and Logarithms Benjamin Peirce. Cases in Equations of the First Degree ... given equation is , indeed , in this case 0 x x + 0 = 0 , an equation which is satisfied by any value whatever of x ...
To which are Added Exponential Equations and Logarithms Benjamin Peirce. Cases in Equations of the First Degree ... given equation is , indeed , in this case 0 x x + 0 = 0 , an equation which is satisfied by any value whatever of x ...
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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