An Elementary Treatise on Algebra: To which are Added Exponential Equations and Logarithms |
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Page 3
... 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 is to be divided by the one which ...
... 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 is to be divided by the one which ...
Page 5
... fourth degree , & c . 16. A polynomial is homogeneous , when all its terms are of the same degree . Thus , 3a - 2b + c is homogeneous of the first degree , 8 a3 b - 16 a2 b2 + b4 is homogeneous of the fourth degree . placed over a 17. A ...
... fourth degree , & c . 16. A polynomial is homogeneous , when all its terms are of the same degree . Thus , 3a - 2b + c is homogeneous of the first degree , 8 a3 b - 16 a2 b2 + b4 is homogeneous of the fourth degree . placed over a 17. A ...
Page 44
... DA : C D : CB : A , & c .; that is , the terms of a proportion may be transposed in any way which is consistent with the application of the test . To find the Fourth Term of a Proportion . 88. 44 [ CH . II . IV . ALGEBRA . 26.
... DA : C D : CB : A , & c .; that is , the terms of a proportion may be transposed in any way which is consistent with the application of the test . To find the Fourth Term of a Proportion . 88. 44 [ CH . II . IV . ALGEBRA . 26.
Page 45
... fourth . Given three terms of a proportion , Solution . The following solution is immediately obtained from the test ... fourth . Ans . BC A ' 2. Given the three first terms of a proportion respectively 2ab2 , 3 a2b , 6b3 ; find the ...
... fourth . Given three terms of a proportion , Solution . The following solution is immediately obtained from the test ... fourth . Ans . BC A ' 2. Given the three first terms of a proportion respectively 2ab2 , 3 a2b , 6b3 ; find the ...
Page 48
... fourth . Likewise , the sum of the first two terms is to their difference , as the sum of the last two is to their dif- ference . Moreover , in finding these sums and differences , both the antecedents may be multiplied by the same ...
... fourth . Likewise , the sum of the first two terms is to their difference , as the sum of the last two is to their dif- ference . Moreover , in finding these sums and differences , both the antecedents may be multiplied by the same ...
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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