An Elementary Treatise on Algebra: To which are Added Exponential Equations and Logarithms |
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Page 6
... difference of these sums preceded by the sign of the greater , may be substituted as a single term for the terms from which it is obtained . When these sums are equal they cancel each other , and the corresponding terms are to be ...
... difference of these sums preceded by the sign of the greater , may be substituted as a single term for the terms from which it is obtained . When these sums are equal they cancel each other , and the corresponding terms are to be ...
Page 8
... difference between two quantities . 26. Problem . To subtract one quantity from another . Solution . Let A denote the aggregate of all the positive terms of the quantity to be subtracted , and B the aggregate of all its negative terms ...
... difference between two quantities . 26. Problem . To subtract one quantity from another . Solution . Let A denote the aggregate of all the positive terms of the quantity to be subtracted , and B the aggregate of all its negative terms ...
Page 12
... a9 b3 + 36 a8 b4 + 54 a7 b5 + 27 a6 b6 by 8 a9b3-36 a8 b4 +54 a7 b5-27 a6 b6 . Ans . 64 a18b6432 a16 b8 +972 a14 610-729 a12 612 , Product of Sum and Difference ; of Homogeneous Quantities . 12 [ CH . I. § IV . ALGEBRA .
... a9 b3 + 36 a8 b4 + 54 a7 b5 + 27 a6 b6 by 8 a9b3-36 a8 b4 +54 a7 b5-27 a6 b6 . Ans . 64 a18b6432 a16 b8 +972 a14 610-729 a12 612 , Product of Sum and Difference ; of Homogeneous Quantities . 12 [ CH . I. § IV . ALGEBRA .
Page 13
... difference is , as in examples 18 and 19 , equal to the difference of their squares . 34. Theorem . The product of homogeneous polynomials is also homogeneous , and the degree of the product is equal to the sum of the degrees of the ...
... difference is , as in examples 18 and 19 , equal to the difference of their squares . 34. Theorem . The product of homogeneous polynomials is also homogeneous , and the degree of the product is equal to the sum of the degrees of the ...
Page 14
... difference of its exponents in the two terms . But when a letter occurs in only one term , it is to be retained in that term , with its exponent unchanged . The required quotient is , then , equal to the quo- tient of the remaining ...
... difference of its exponents in the two terms . But when a letter occurs in only one term , it is to be retained in that term , with its exponent unchanged . The required quotient is , then , equal to the quo- tient of the remaining ...
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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