An Elementary Treatise on Algebra: To which are Added Exponential Equations and LogarithmsJames Munroe, 1858 - 284 páginas |
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Página 2
... unity . Thus , in the expression 15 a b , 15 is the numerical co- efficient of a b ; and , in the expression xy , 1 may be re- garded as the coefficient of xy . 6. The continued product of a quantity multiplied repeatedly by itself , is ...
... unity . Thus , in the expression 15 a b , 15 is the numerical co- efficient of a b ; and , in the expression xy , 1 may be re- garded as the coefficient of xy . 6. The continued product of a quantity multiplied repeatedly by itself , is ...
Página 3
... unity . Thus the fifth power of a is written a3 ; but when a stands by itself , it may be regarded as a1 . 7. The root of a quantity is the quantity which , multiplied a certain number of times by itself , pro- duces the given quantity ...
... unity . Thus the fifth power of a is written a3 ; but when a stands by itself , it may be regarded as a1 . 7. The root of a quantity is the quantity which , multiplied a certain number of times by itself , pro- duces the given quantity ...
Página 14
... unity , the quotient is simply equal to the remaining portion of the dividend . The sign of the quotient must , from art . 30 , be the same as that of the divisor when the dividend is positive , and it must be the reverse of that of the ...
... unity , the quotient is simply equal to the remaining portion of the dividend . The sign of the quotient must , from art . 30 , be the same as that of the divisor when the dividend is positive , and it must be the reverse of that of the ...
Página 16
... unity . Whence any quantity with an exponent equal to zero is unity . Thus , amamao : = : 1 . 38. Corollary . When , in example 6 of art . 30 , the ex- ponent n of a in the divisor is greater than its exponent m in the dividend , the ...
... unity . Whence any quantity with an exponent equal to zero is unity . Thus , amamao : = : 1 . 38. Corollary . When , in example 6 of art . 30 , the ex- ponent n of a in the divisor is greater than its exponent m in the dividend , the ...
Página 23
... unity and increasing that of b by unity ; and the number of terms is equal to the exponent n . 51. Corollary . If b is put equal to a in the preceding quotient , each of its terms becomes equal to an − 1 , which gives the peculiar ...
... unity and increasing that of b by unity ; and the number of terms is equal to the exponent n . 51. Corollary . If b is put equal to a in the preceding quotient , each of its terms becomes equal to an − 1 , which gives the peculiar ...
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.