An Elementary Treatise on Algebra: To which are Added Exponential Equations and LogarithmsJames Munroe and Company, 1860 - 284 páginas |
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Página 6
... obtained . When these sums are equal they cancel each other , and the corresponding terms are to be omitted . Thus , a2b - 9 a b2 +8 a2b + 5c - 3 a2 b + 8 a b2 + 2 a2b + c + ab2 . 8 c is the same as 8 a2 b — 2 c . - 21. EXAMPLES . 1 ...
... obtained . When these sums are equal they cancel each other , and the corresponding terms are to be omitted . Thus , a2b - 9 a b2 +8 a2b + 5c - 3 a2 b + 8 a b2 + 2 a2b + c + ab2 . 8 c is the same as 8 a2 b — 2 c . - 21. EXAMPLES . 1 ...
Página 7
... obtained can be reduced to its simplest form by art . 20 . 24. EXAMPLES . 1. Find the sum of a and a . 2. Find the sum of 11 x and 9 x . Ans . 2 a . Ans . 20 x . 3. Find the sum of 11 x and 4. Find the sum of 9 x . 11 x and 9 x . - 9 x ...
... obtained can be reduced to its simplest form by art . 20 . 24. EXAMPLES . 1. Find the sum of a and a . 2. Find the sum of 11 x and 9 x . Ans . 2 a . Ans . 20 x . 3. Find the sum of 11 x and 4. Find the sum of 9 x . 11 x and 9 x . - 9 x ...
Página 8
... obtained by increasing C - A by the excess of A above A — B , that is , by B , and it is thus found to be C - A + B . The same result would be obtained by adding to C the quantity AB , with its signs reversed , so as to make it -AB ...
... obtained by increasing C - A by the excess of A above A — B , that is , by B , and it is thus found to be C - A + B . The same result would be obtained by adding to C the quantity AB , with its signs reversed , so as to make it -AB ...
Página 11
... obtained from the product of the negative term of one factor by the positive term of the other , as ― C by B or Hence , -D by A. The product of two polynomials is obtained by multiplying each term of one factor by each term of the other ...
... obtained from the product of the negative term of one factor by the positive term of the other , as ― C by B or Hence , -D by A. The product of two polynomials is obtained by multiplying each term of one factor by each term of the other ...
Página 13
... obtained ; and , therefore , by art . 15 , the degree of each term of the product is equal to the sum of the degrees of the factors . Thus , in example 16 , the degree of each factor is 12 , and that of the product is 12 + 12 or 24 ...
... obtained ; and , therefore , by art . 15 , the degree of each term of the product is equal to the sum of the degrees of the factors . Thus , in example 16 , the degree of each factor is 12 , and that of the product is 12 + 12 or 24 ...
Outras edições - Ver tudo
An Elementary Treatise on Algebra: To which are Added Exponential Equations ... Benjamin Peirce Visualização integral - 1858 |
An Elementary Treatise on Algebra: To which are Added Exponential Equations ... Benjamin Peirce Visualização integral - 1837 |
An Elementary Treatise on Algebra: To which are Added Exponential Equations ... Benjamin Peirce Visualização integral - 1837 |
Palavras e frases frequentes
126 become zero 3d root approximate values coefficient commensurable roots contain continued fraction continued product Corollary courier decimals deficient terms denote derivative dividend equal roots equal to zero Find the 3d Find the continued Find the greatest Find the square Find the sum Free the equation gallons given equation gives greatest common divisor Hence last term least common multiple letter logarithm monomials Multiply negative exponents nth root number of real number of terms Obtain one equation positive roots preceding article Problem proportion quantities in example Questions into Equations quotient radical quantities ratio real roots reduced remainder required equation required number row of signs Scholium Solution Solve the equation square root Sturm's Theorem substitution subtracted suppressed Theorem three equations unity unknown quan unknown quantity whence wine
Passagens conhecidas
Página 48 - In any proportion the terms are in proportion by Composition and Division ; that is, the sum of the first two terms is to their difference, as the sum of the last two terms is to their difference.
Página 55 - There is a number consisting of two digits, the second of which is greater than the first, and if the number be divided by the sum of its digits, the quotient is 4...
Página 130 - The rule of art. 28, applied to this case, in which the factors are all equal, gives for. the coefficient of the required power the same power of the given coefficient, and for the exponent of each letter the given exponent added to itself as many times as there are units in the exponent of the required power. Hence...
Página 127 - Multiply the divisor, thus increased, by the last figure of the root; subtract the product from the dividend, and to the remainder bring down the next period for a new dividend.
Página 159 - A certain capital is let at 4 per cent. ; if we multiply the number of dollars in the capital, by the number of dollars in the interest for 5 months, we obtain 11?041§.
Página 172 - Ans. 15 and 26. 31. What two numbers are they, whose sum is a, and the sum of whose squares is b 1 Ans.
Página 232 - An equation of any degree whatever cannot have a greater number of positive roots than there are variations in the signs of Us terms, nor a greater number of negative roots than there are permanences of these signs.
Página 63 - A term may be transposed from one member of an equation to the other by changing its sign.
Página 45 - Given three terms of a proportion, to find the fourth. Solution. The following solution is immediately obtained from the test. When the required term is an extreme, divide the product of the means by the given extreme, and the quotient is the required extreme. When the required term is a mean, divide the product of the extremes by the given mean, and the quotient is the required mean.
Página 196 - Hence, to find the sum, multiply the first term by the difference between unity and that power of the ratio whose exponent is equal to the number of terms, and divide the product by the difference between unity and the ratio. Examples in Geometrical Progression.