An Elementary Treatise on Algebra: To which are Added Exponential Equations and LogarithmsJames Munroe, 1858 - 284 páginas |
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Página 22
... integral pos- itive powers of the same degree is divisible by the difference of their roots . an b " is divisible by a- - b . - Thus , Demonstration . Divide an - bn by a - b , as in art . 42 , proceeding only to the first remainder ...
... integral pos- itive powers of the same degree is divisible by the difference of their roots . an b " is divisible by a- - b . - Thus , Demonstration . Divide an - bn by a - b , as in art . 42 , proceeding only to the first remainder ...
Página 124
... integral power contained in the left hand period ; and the root of this power is the left hand figure of the required root , and is just as many places distant from the decimal point as the corresponding period is removed by periods ...
... integral power contained in the left hand period ; and the root of this power is the left hand figure of the required root , and is just as many places distant from the decimal point as the corresponding period is removed by periods ...
Página 141
... integral powers of x are written in the second member , because the product could , evidently , give no others , and all the positive integral powers of x are included , because the coefficients of any which are super- fluous must be ...
... integral powers of x are written in the second member , because the product could , evidently , give no others , and all the positive integral powers of x are included , because the coefficients of any which are super- fluous must be ...
Página 173
... integral or frac- tional . 235. EXAMPLES . 1. Solve the equation A x2n + B x + M = 0 Solution . If the square is completed , as in the preceding article , and the square root extracted , the result is Ax " + B = ± √ ( ~ AM + B2 ) ...
... integral or frac- tional . 235. EXAMPLES . 1. Solve the equation A x2n + B x + M = 0 Solution . If the square is completed , as in the preceding article , and the square root extracted , the result is Ax " + B = ± √ ( ~ AM + B2 ) ...
Página 240
... 1 is when x- - 1 it is , − + , - , + , - , + ‚ —‚— ‚ + , - , + ; - + ,一,一, so that the number of these roots cannot exceed 8 . Integral Root . Again , when x is infinitely little 240 [ CH . VIII . § III . ALGEBRA .
... 1 is when x- - 1 it is , − + , - , + , - , + ‚ —‚— ‚ + , - , + ; - + ,一,一, so that the number of these roots cannot exceed 8 . Integral Root . Again , when x is infinitely little 240 [ CH . VIII . § III . ALGEBRA .
Outras edições - Ver tudo
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.