An Elementary Treatise on Algebra: To which are Added Exponential Equations and LogarithmsJames Munroe, 1858 - 284 páginas |
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Página 22
... true for any power , as the ( n - 1 ) st , it also holds for the nth , or the next greater . But from examples , 10 , 11 , 12 , 13 of art . 43 , the propo- sition holds for the 2d , 3d , 4th , and 5th ; and therefore it must be true for ...
... true for any power , as the ( n - 1 ) st , it also holds for the nth , or the next greater . But from examples , 10 , 11 , 12 , 13 of art . 43 , the propo- sition holds for the 2d , 3d , 4th , and 5th ; and therefore it must be true for ...
Página 75
... true solution ; and sometimes it indicates an impossibility in the proposed question . In any such case , therefore , it is necessary to return to the data of the problem and investigate the signification of this result . 128. EXAMPLES ...
... true solution ; and sometimes it indicates an impossibility in the proposed question . In any such case , therefore , it is necessary to return to the data of the problem and investigate the signification of this result . 128. EXAMPLES ...
Página 76
... true solution . 4. In what cases would the value of one of the unknown quantities in example 39 of art . 126 become zero ? and what would this value signify ? Ans . When bna , or = ma ; and these equations indicate that a is itself such ...
... true solution . 4. In what cases would the value of one of the unknown quantities in example 39 of art . 126 become zero ? and what would this value signify ? Ans . When bna , or = ma ; and these equations indicate that a is itself such ...
Página 81
... true solution of the problem ; and if the solution gives no other than negative values for this quantity , the problem is generally impossible . But , in this case , the negative of the negative value of the unknown quantity is positive ...
... true solution of the problem ; and if the solution gives no other than negative values for this quantity , the problem is generally impossible . But , in this case , the negative of the negative value of the unknown quantity is positive ...
Página 83
... true solutions . 5. In what cases would the values of either of the un- known quantities in example 38 of art . 126 be negative ? why should this be the case ? and could the enunciation be corrected for this case ? Ans . If we suppose ...
... true solutions . 5. In what cases would the values of either of the un- known quantities in example 38 of art . 126 be negative ? why should this be the case ? and could the enunciation be corrected for this case ? Ans . If we suppose ...
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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 arithmetical progression Binomial Theorem coefficient commensurable roots common difference contained continued fraction continued product Corollary deficient terms denote derivative Divide dividend division equal roots 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
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 268 - The logarithm of any power of a number is equal to the logarithm of the number multiplied by the exponent of the power.
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 127 - Multiply the divisor, thus augmented, by the last figure of the root, and subtract the product from the dividend, and to the remainder bring down the next period for a new dividend. V. Double the whole root already found, for a new divisor, and continue the operation as before, until all the periods are brought down.
Página 192 - One hundred stones being placed on the ground in a straight line, at the distance of 2 yards from each other, how far will a person travel who shall bring them one by one to a basket, placed at 2 yards from the first stone ? Ans.
Página 268 - The logarithm of the quotient is equal to the logarithm of the dividend, diminished by the logarithm of the divisor.
Página 63 - A term may be transposed from one member of an equation to the other by changing its sign.
Página 130 - ... as many times as there are units in the exponent of the required power. Hence...
Página 32 - The 2d line of col. 1 is the 1st line multiplied by 7 in order to render its first term divisible by the first term of the new divisor ; the remainder of the division is the 4th line of col.
Página 1 - Definitions and Notation. 1. Algebra, according to the usual definition, is that branch of mathematics in which the quantities considered are represented by the letters of the alphabet, and the operations to be performed upon them are indicated by signs. In this sense it would embrace almost the whole science of mathematics, elementary geometry alone being excepted. It is, consequently, subject in common use to some limitations, which will be more easily understood, when we are advanced in the science.