An Elementary Treatise on Algebra: To which are Added Exponential Equations and Logarithms |
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Page 8
... result would be obtained by adding to C the quantity AB , with its signs reversed , so as to make it -A + B . Hence , To subtract one quantity from another , change the signs of the quantity to be subtracted from to— , Multiplication of ...
... result would be obtained by adding to C the quantity AB , with its signs reversed , so as to make it -A + B . Hence , To subtract one quantity from another , change the signs of the quantity to be subtracted from to— , Multiplication of ...
Page 11
... + , while the product of two terms which have contrary signs is to be affected by the sign The result is to be reduced as in art . 20 . - Multiplication of Polynomials . 31. EXAMPLES . 1. Multiply 22+ CH . I. § IV . ] 11 MULTIPLICATION .
... + , while the product of two terms which have contrary signs is to be affected by the sign The result is to be reduced as in art . 20 . - Multiplication of Polynomials . 31. EXAMPLES . 1. Multiply 22+ CH . I. § IV . ] 11 MULTIPLICATION .
Page 23
... result an n α = nan - 1 52. There are sometimes two or more terms in the divisor , or in the dividend , or in both , which contain the same highest power of the letter accord- ing to which the terms are arranged . In this case , these ...
... result an n α = nan - 1 52. There are sometimes two or more terms in the divisor , or in the dividend , or in both , which contain the same highest power of the letter accord- ing to which the terms are arranged . In this case , these ...
Page 47
... results to the proportion gives whence A : BC : D , A + C : B + D = A : B = C : D A - C : B - D = A : B = C : D mA + nCm B ÷ nD = A : B = C : D mA - n C : m B - n D - A : B = C : D ; A + C : B + D = A - C : B - D mA + nCm B ÷ nD = mA - n C ...
... results to the proportion gives whence A : BC : D , A + C : B + D = A : B = C : D A - C : B - D = A : B = C : D mA + nCm B ÷ nD = A : B = C : D mA - n C : m B - n D - A : B = C : D ; A + C : B + D = A - C : B - D mA + nCm B ÷ nD = mA - n C ...
Page 49
... result AXE : BX F = CX G : DXH is a new proportion . 99. Likewise , all the terms of a proportion may be raised to the same power . Thus , gives A : B C : D A2 : B2 = = C2 : D2 √A : √B = √✓C : ✓D Am Bm Cm : Dm m m m m √A : √B ...
... result AXE : BX F = CX G : DXH is a new proportion . 99. Likewise , all the terms of a proportion may be raised to the same power . Thus , gives A : B C : D A2 : B2 = = C2 : D2 √A : √B = √✓C : ✓D Am Bm Cm : Dm m m m m √A : √B ...
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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