An Elementary Treatise on Algebra: To which are Added Exponential Equations and Logarithms |
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Page 16
... means of negative exponents without using frac- tional forms . 39. EXAMPLES . 1. Divide 5 a4 b3 c2 d by 15 a b5 c2 d3 e2 . Ans . 3-1 a3 b - 2d - 2e - 2 2. Divide 6 a b by 9 a b7 . Ans . a b - 62.3 − 1 ao b − 6 . 3. Divide 1 by 8 a11 b ...
... means of negative exponents without using frac- tional forms . 39. EXAMPLES . 1. Divide 5 a4 b3 c2 d by 15 a b5 c2 d3 e2 . Ans . 3-1 a3 b - 2d - 2e - 2 2. Divide 6 a b by 9 a b7 . Ans . a b - 62.3 − 1 ao b − 6 . 3. Divide 1 by 8 a11 b ...
Page 21
... means of negative exponents any mono- mial may be taken out as a factor of a quantity . 48. EXAMPLES . 1. Take out 3 a2b as a factor of 15 a5 b2 + 6 a3 b + 9a2 b2 + 3 a2 b . Ans . 3 a2b ( 5 a3b + 2a + 3b + 1 ) . 2. Take out am as a ...
... means of negative exponents any mono- mial may be taken out as a factor of a quantity . 48. EXAMPLES . 1. Take out 3 a2b as a factor of 15 a5 b2 + 6 a3 b + 9a2 b2 + 3 a2 b . Ans . 3 a2b ( 5 a3b + 2a + 3b + 1 ) . 2. Take out am as a ...
Page 40
... means of art . 73 . 79 . EXAMPLES . C 1. Multiply together , and e ace Ans . F bdf 6 a3 b5 3 a2 d3 2. Multiply by 7 d8 69 265 e 9 a5 Ans . 7d5 e10 ° Product and Quotient of Fractions . Reciprocal . 3. Multiply 40 § III . ALGEBRA . [ CH ...
... means of art . 73 . 79 . EXAMPLES . C 1. Multiply together , and e ace Ans . F bdf 6 a3 b5 3 a2 d3 2. Multiply by 7 d8 69 265 e 9 a5 Ans . 7d5 e10 ° Product and Quotient of Fractions . Reciprocal . 3. Multiply 40 § III . ALGEBRA . [ CH ...
Page 42
... means , a fraction can be freed from nega- tive exponents . 83 . EXAMPLES . 1. Free the fraction a - 3b2 d - le from ... Means equals that of Extremes . 1 + 42 [ CH . II . § III . ALGEBRA .
... means , a fraction can be freed from nega- tive exponents . 83 . EXAMPLES . 1. Free the fraction a - 3b2 d - le from ... Means equals that of Extremes . 1 + 42 [ CH . II . § III . ALGEBRA .
Page 43
... 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 , reduced to ...
... 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 , reduced to ...
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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