An Elementary Treatise on Algebra: To which are Added Exponential Equations and LogarithmsJames Munroe, 1858 - 284 páginas |
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Página 2
... negative sign , and placed between two quantities denotes that the quantity which follows it is to be subtracted from the one which precedes it . Thus 7-2 is 7 minus or less 2 and denotes the remain . der after subtracting 2 from 7 ...
... negative sign , and placed between two quantities denotes that the quantity which follows it is to be subtracted from the one which precedes it . Thus 7-2 is 7 minus or less 2 and denotes the remain . der after subtracting 2 from 7 ...
Página 6
... negative terms . When the first term is not preceded by any sign it is to be regarded as positive . 20. The following rule for reducing polynomials , which contain similar terms , is too obvious to require demonstration . Find the sum ...
... negative terms . When the first term is not preceded by any sign it is to be regarded as positive . 20. The following rule for reducing polynomials , which contain similar terms , is too obvious to require demonstration . Find the sum ...
Página 8
... negative terms ; then A B is the quantity to be subtracted , and let C denote the quantity from which it is to be taken . --- If A alone be taken from C , the remainder C - A is as much too small as the quantity subtracted is too large ...
... negative terms ; then A B is the quantity to be subtracted , and let C denote the quantity from which it is to be taken . --- If A alone be taken from C , the remainder C - A is as much too small as the quantity subtracted is too large ...
Página 11
... negative terms C and - - - negative terms of the product , as BC and - D ; but the AD , are obtained from the product of the negative term of one factor by the positive term of the other , as -C by B or -D by A. Hence , The product of ...
... negative terms C and - - - negative terms of the product , as BC and - D ; but the AD , are obtained from the product of the negative term of one factor by the positive term of the other , as -C by B or -D by A. Hence , The product of ...
Página 13
... negative factors is even ; and it is negative , as in example 10 , when the number of negative factors is odd . 33. Corollary . The product of the sum of two numbers by their difference is , as in examples 18 and 19 , equal to the ...
... negative factors is even ; and it is negative , as in example 10 , when the number of negative factors is odd . 33. Corollary . The product of the sum of two numbers by their difference is , as in examples 18 and 19 , equal to the ...
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 - 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.