An Elementary Treatise on Algebra: To which are Added Exponential Equations and LogarithmsJames Munroe, 1858 - 284 páginas |
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Página 27
... greatest com- mon factor or divisor . 57. Problem . To find the greatest common di- visor of several monomials . Solution . It is equal to the product of the greatest common divisor of the coefficients , by those different literal ...
... greatest com- mon factor or divisor . 57. Problem . To find the greatest common di- visor of several monomials . Solution . It is equal to the product of the greatest common divisor of the coefficients , by those different literal ...
Página 28
... find the greatest common divi- sor of any two quantities . Solution . Divide the greater quantity by the less , and the remainder , which is less than either of the given quantities , is , by the preceding article , divisible by the ...
... find the greatest common divi- sor of any two quantities . Solution . Divide the greater quantity by the less , and the remainder , which is less than either of the given quantities , is , by the preceding article , divisible by the ...
Página 29
... Find the greatest common divisor of 1825 and 1995 Solution . 1995 | 1825 1825 1 1825 170 , 1st Rem . 1700 10 170 125 , 2d Rem . 125 1 125 | 45 , 3d Rem . 90 2 45 35 , 4th Rem . 35 1 35 10 , 5th Rem . 30 3 1015 , 6th Rem . 10 2 Ans . 5 ...
... Find the greatest common divisor of 1825 and 1995 Solution . 1995 | 1825 1825 1 1825 170 , 1st Rem . 1700 10 170 125 , 2d Rem . 125 1 125 | 45 , 3d Rem . 90 2 45 35 , 4th Rem . 35 1 35 10 , 5th Rem . 30 3 1015 , 6th Rem . 10 2 Ans . 5 ...
Página 30
... Find the greatest common divisor of 13212 and 1851 . Ans . 3 . 3. Find the greatest common divisor of 1221 and 333 . Ans . 111 . 63. The above rule requires some modification in its application to polynomials . Thus it frequently ...
... Find the greatest common divisor of 13212 and 1851 . Ans . 3 . 3. Find the greatest common divisor of 1221 and 333 . Ans . 111 . 63. The above rule requires some modification in its application to polynomials . Thus it frequently ...
Página 31
... Find the greatest common divisor of 6 a2 x3 + 21 a3 x2 27 a5 and 4 x4 + 5 a2 x2 + 21 a3 x . Solution . These quantities have no common monomial factor ; but the monomial factor 3 a common to all the terms of the first of them , and the ...
... Find the greatest common divisor of 6 a2 x3 + 21 a3 x2 27 a5 and 4 x4 + 5 a2 x2 + 21 a3 x . Solution . These quantities have no common monomial factor ; but the monomial factor 3 a common to all the terms of the first of them , and the ...
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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.