An Elementary Treatise on Algebra: To which are Added Exponential Equations and LogarithmsJ. Munroe, 1837 - 284 páginas |
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Página 6
... demonstration . Find the sum of the similar positive terms by add- ing their coefficients , and in the same way the sum of their similar negative terms . The difference of these sums preceded by the sign of the greater , may be ...
... demonstration . Find the sum of the similar positive terms by add- ing their coefficients , and in the same way the sum of their similar negative terms . The difference of these sums preceded by the sign of the greater , may be ...
Página 13
... Demonstration . For the number of factors in each term of the product is equal to the sum of the numbers of factors in all the terms from which it is obtained ; and , therefore , by art . 15 , the degree of each term of the product is ...
... Demonstration . For the number of factors in each term of the product is equal to the sum of the numbers of factors in all the terms from which it is obtained ; and , therefore , by art . 15 , the degree of each term of the product is ...
Página 22
... Demonstration . Divide an - bn by a - b , as in art . 34 , proceeding only to the first remainder , as follows . an a . ― bn an 1st Remainder = an - 1b or as in example 4 , of art . 36 . a -- b -1 ban - 1 bn n ; _b , — 1st Remainder an ...
... Demonstration . Divide an - bn by a - b , as in art . 34 , proceeding only to the first remainder , as follows . an a . ― bn an 1st Remainder = an - 1b or as in example 4 , of art . 36 . a -- b -1 ban - 1 bn n ; _b , — 1st Remainder an ...
Página 25
... Demonstration . For dividing both these terms by a quan- tity is the same as striking out a factor common to the two terms of a quotient , which , as is evident from art . 30 , does not affect the value of the quotient . Also ...
... Demonstration . For dividing both these terms by a quan- tity is the same as striking out a factor common to the two terms of a quotient , which , as is evident from art . 30 , does not affect the value of the quotient . Also ...
Página 26
... Demonstration . Let the greatest of the two quantities be A , and the least B ; let the entire part of their quotient after division be Q , and the remainder R ; and let the greatest Greatest Common Divisor . common divisor of A and B ...
... Demonstration . Let the greatest of the two quantities be A , and the least B ; let the entire part of their quotient after division be Q , and the remainder R ; and let the greatest Greatest Common Divisor . common divisor of A and B ...
Outras edições - Ver tudo
An Elementary Treatise on Algebra: To which are Added Exponential Equations ... Benjamin Peirce Visualização integral - 1860 |
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 |
Palavras e frases frequentes
3d root 94 become zero arithmetical progression Binomial Theorem coefficient commensurable roots common difference continued fraction continued product Corollary deficient terms Demonstration denote dividend divisible equal roots equal to zero equation becomes equation x3 factor Find the 3d Find the 4th Find the continued Find the greatest Find the square Find the sum Free the equation gallons Geometrical Progression given equation given number gives greatest common divisor Hence imaginary roots integer last term least common multiple letter logarithm monomials negative roots number of real number of terms obtained places of decimals polynomial positive roots preceding article Problem quantities in example quotient radical quantities ratio real root reduced remainder required equation Scholium Second Degree Solution Solve the equation square root subtracted tained term multiplied tity unity unknown quantity whence
Passagens conhecidas
Página 47 - 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 54 - 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 149 - 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 197 - Problem. To find the last term of an arithmetical progression when its first term, common difference, and number of terms are known. Solution. In this case a, r, and n are supposed to be known, and I is to be found.
Página 262 - The logarithm of any power of a number is equal to the logarithm of the number multiplied by the exponent of the power.
Página 62 - A term may be transposed from one member of an equation to the other by changing its sign.
Página 44 - Arrange the terms in the statement so that the causes shall compose one couplet, and the effects the other, putting ( ) in the place of the required term. II. If the required term be an extreme, divide the product of the means by the given extreme ; if the required farm be a mean, divide the product of the extremes by the given mean.
Página 46 - Likewise, the sum of the antecedents is to their difference, as the sum of the consequents is to their difference.
Página 99 - What fraction is that, whose numerator being doubled, and denominator increased by 7, the value becomes §; but the denominator being doubled, and the numerator increased by 2, the value becomes f?
Página 206 - The sum of the squares of the extremes of four numbers in arithmetical progression is 200, and the sum of the squares of the means is 136. What are the numbers ? Ans.
Referências a este livro
The Emergence of the American Mathematical Research Community, 1876-1900: J ... Karen Hunger Parshall,David E. Rowe Pré-visualização limitada - 1994 |