An Elementary Treatise on Algebra: To which are Added Exponential Equations and LogarithmsJ. Munroe, 1837 - 284 páginas |
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Página 21
... known , by dividing by the known factor , and the quotient is the other factor . And when a letter occurs as a factor of all the terms of a quantity , it is a factor of the quantity , and may be taken out as a factor , with an exponent ...
... known , by dividing by the known factor , and the quotient is the other factor . And when a letter occurs as a factor of all the terms of a quantity , it is a factor of the quantity , and may be taken out as a factor , with an exponent ...
Página 64
... known quantities , whether positive or negative , and x is the unknown quantity . Demonstration . When an equation of the first degree with one unknown quantity is reduced , as in art . 88 , its first member is composed of two classes ...
... known quantities , whether positive or negative , and x is the unknown quantity . Demonstration . When an equation of the first degree with one unknown quantity is reduced , as in art . 88 , its first member is composed of two classes ...
Página 65
... known terms to the second member , and all its unknown terms to the first member ; and the value of the unknown quantity is equal to the quotient arising from the division of the second member by the multiplier of the unknown quantity ...
... known terms to the second member , and all its unknown terms to the first member ; and the value of the unknown quantity is equal to the quotient arising from the division of the second member by the multiplier of the unknown quantity ...
Página 77
... known quantity , and that it may have any value whatever . In some cases , however , there are limita- tions to the change of value of the unknown quan- tity . EXAMPLES . 1. In what case would both the terms of the fractional value of ...
... known quantity , and that it may have any value whatever . In some cases , however , there are limita- tions to the change of value of the unknown quan- tity . EXAMPLES . 1. In what case would both the terms of the fractional value of ...
Página 78
... known quantity . But , in this case , all the algebraic values of the unknown quantity but the first become infi- nite , as they should , because they are obtained on the supposition that the second body has passed round the circle once ...
... known quantity . But , in this case , all the algebraic values of the unknown quantity but the first become infi- nite , as they should , because they are obtained on the supposition that the second body has passed round the circle once ...
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 |
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 |