An Elementary Treatise on Algebra: To which are Added Exponential Equations and Logarithms |
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Page 3
... third or cube root of a , 4 Va is the fourth root of a , n ✓a is the nth root of a . 8. The signs and are called the signs of di- vision , and either of them placed between two quan- tities denotes that the quantity which precedes it ...
... third or cube root of a , 4 Va is the fourth root of a , n ✓a is the nth root of a . 8. The signs and are called the signs of di- vision , and either of them placed between two quan- tities denotes that the quantity which precedes it ...
Page 34
... + 2x +1 +2 -1 - y2 y 2 -2x | y2—2x | y + 4x - y2 -2y y + 2 +1 +1 2 --- xy - 2x y 2 +1 +2 y y + 2 1 Ans . ( y + 2 ) ( x2 + 3 x ) y = ( x2 + 3x ) ( y2 + 2y ) . Greatest Common Divisor . The third line of col . 34 [ CH . II . § I. ALGEBRA .
... + 2x +1 +2 -1 - y2 y 2 -2x | y2—2x | y + 4x - y2 -2y y + 2 +1 +1 2 --- xy - 2x y 2 +1 +2 y y + 2 1 Ans . ( y + 2 ) ( x2 + 3 x ) y = ( x2 + 3x ) ( y2 + 2y ) . Greatest Common Divisor . The third line of col . 34 [ CH . II . § I. ALGEBRA .
Page 35
... third line of col . 1 is the remainder of the division of the 1st line of col . 1 by the 1st line of col . 2 ; and this remainder , reduced by the suppression of the factor x is the 4th line of col . 1. The 5th line of col . 2 is the ...
... third line of col . 1 is the remainder of the division of the 1st line of col . 1 by the 1st line of col . 2 ; and this remainder , reduced by the suppression of the factor x is the 4th line of col . 1. The 5th line of col . 2 is the ...
Page 43
... third its means . Thus , A and D are the extremes of this proportion , and B and C its means . 86. If the ratios of the preceding proportion are reduced to a common consequent , in the same way in which frac- tions are , by art . 67 ...
... third its means . Thus , A and D are the extremes of this proportion , and B and C its means . 86. If the ratios of the preceding proportion are reduced to a common consequent , in the same way in which frac- tions are , by art . 67 ...
Page 44
... third , these four quantities form a proportion . Demonstration . Let A , B , C , D be four quantities such that AX D B x C. = We have , by dividing B x D , A x D : B x D = BX C : B x D , or , by reducing these ratios to lower terms ...
... third , these four quantities form a proportion . Demonstration . Let A , B , C , D be four quantities such that AX D B x C. = We have , by dividing B x D , A x D : B x D = BX C : B x D , or , by reducing these ratios to lower terms ...
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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