An Elementary Treatise on Algebra: To which are Added Exponential Equations and Logarithms |
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Page 15
... give + ; unlike signs give — . 36. EXAMPLES . 136 1. Divide 65 a b by 5 a . Ans . = 13 b . 1 2. Divide 132 a5 63 c by 11 a3 b3 . Ans . - - 12 a2 c . 3. Divide 144 a b3 c2 d e by - 112 a b c e1 h . Ans . 9 c d8 7be6 h 27 4. Divide - 135 ...
... give + ; unlike signs give — . 36. EXAMPLES . 136 1. Divide 65 a b by 5 a . Ans . = 13 b . 1 2. Divide 132 a5 63 c by 11 a3 b3 . Ans . - - 12 a2 c . 3. Divide 144 a b3 c2 d e by - 112 a b c e1 h . Ans . 9 c d8 7be6 h 27 4. Divide - 135 ...
Page 23
... gives the peculiar 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 ...
... gives the peculiar 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 ...
Page 31
... all the terms of the first of them , and the factor x common to all the terms of the second , being suppressed in columns 1 and Greatest Common Divisor . 2 , give the first lines CH . II . § 1. ] 31 REDUCTION OF FRACTIONS .
... all the terms of the first of them , and the factor x common to all the terms of the second , being suppressed in columns 1 and Greatest Common Divisor . 2 , give the first lines CH . II . § 1. ] 31 REDUCTION OF FRACTIONS .
Page 32
... give the first lines of the following form of the process , which is similar to that in art . 62 . Col. 1 . 2 x37 a x2 - 9 a3 14x349 a x2- 63 a3 Col. 2 . 4x3 +5 a2 x +21 a3 Col. 3 . 2 -x a3 4x3 +14 a x2 - 18 a3 14 x3 - 5 a x2 - 39 a2x ...
... give the first lines of the following form of the process , which is similar to that in art . 62 . Col. 1 . 2 x37 a x2 - 9 a3 14x349 a x2- 63 a3 Col. 2 . 4x3 +5 a2 x +21 a3 Col. 3 . 2 -x a3 4x3 +14 a x2 - 18 a3 14 x3 - 5 a x2 - 39 a2x ...
Page 33
... gives 7 a2 b ( x - 2 a ) for the required greatest common divisor . - - a3 and Ans . x - a . 3. Find the greatest common divisor of x3 x2 - a2 . V 4. Find the greatest common divisor of 15 63 and 3 a3 + 6 a2 b + 6 a b2 + 363 . 5 a3 — 10 ...
... gives 7 a2 b ( x - 2 a ) for the required greatest common divisor . - - a3 and Ans . x - a . 3. Find the greatest common divisor of x3 x2 - a2 . V 4. Find the greatest common divisor of 15 63 and 3 a3 + 6 a2 b + 6 a b2 + 363 . 5 a3 — 10 ...
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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