An Elementary Treatise on Algebra: To which are Added Exponential Equations and LogarithmsJ. Munroe, 1837 - 284 páginas |
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Página 8
... remainder C A is as much too small as the quantity subtracted is too large , that is , as much as A is larger than A - B . The required re- mainder is , consequently , obtained by increasing C — A by the excess of A above A B , that is ...
... remainder C A is as much too small as the quantity subtracted is too large , that is , as much as A is larger than A - B . The required re- mainder is , consequently , obtained by increasing C — A by the excess of A above A B , that is ...
Página 18
... remainder must be equal to the sum of the products of the divisor by the remaining terms of the quotient , and may be used as a new dividend to obtain another term of the quo- tient . By pursuing this process until the dividend is en ...
... remainder must be equal to the sum of the products of the divisor by the remaining terms of the quotient , and may be used as a new dividend to obtain another term of the quo- tient . By pursuing this process until the dividend is en ...
Página 19
... remainder from which it is obtained , and is subtracted from this dividend or remainder . 64x6 — 16 a3 x3 + a6 | 4x2 - 4 ax + a2 = Divisor . 64x6-64 a x5 + 16a2x2 16x1 + 16 a x3 + 12a2x2 + 4a3x + aa 16 a3 x3 + a6 1st Remainder . 64 a x5 ...
... remainder from which it is obtained , and is subtracted from this dividend or remainder . 64x6 — 16 a3 x3 + a6 | 4x2 - 4 ax + a2 = Divisor . 64x6-64 a x5 + 16a2x2 16x1 + 16 a x3 + 12a2x2 + 4a3x + aa 16 a3 x3 + a6 1st Remainder . 64 a x5 ...
Página 22
... remainder , as follows . an a . ― bn an 1st Remainder = an - 1b or as in example 4 , of art . 36 . a -- b -1 ban - 1 bn n ; _b , — 1st Remainder an - 1b — bn = b ( an — 1 — bn —1 ) . Now , if the factor an — 1— bn - 1 of this remainder ...
... remainder , as follows . an a . ― bn an 1st Remainder = an - 1b or as in example 4 , of art . 36 . a -- b -1 ban - 1 bn n ; _b , — 1st Remainder an - 1b — bn = b ( an — 1 — bn —1 ) . Now , if the factor an — 1— bn - 1 of this remainder ...
Página 26
... remainder after division . Demonstration . Let the greatest of the two quantities be A , and the least B ; let the entire part of their quotient after division be Q , and the remainder R ; and let the greatest Greatest Common Divisor ...
... remainder after division . Demonstration . Let the greatest of the two quantities be A , and the least B ; let the entire part of their quotient after division be Q , and the remainder R ; and let the greatest Greatest Common Divisor ...
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 - 1858 |
An Elementary Treatise on Algebra: To which are Added Exponential Equations ... Benjamin Peirce Visualização integral - 1837 |
Palavras e frases frequentes
3d root 94 become zero arithmetical progression Binomial Theorem coefficient commensurable roots common difference continued fraction continued product Corollary deficient terms Demonstration denote dividend divisible equal roots equal to zero equation becomes equation x3 factor Find the 3d Find the 4th Find the continued Find the greatest Find the square Find the sum Free the equation gallons Geometrical Progression given equation given number gives greatest common divisor Hence imaginary roots integer last term least common multiple letter logarithm monomials negative roots number of real number of terms obtained places of decimals polynomial positive roots preceding article Problem quantities in example quotient radical quantities ratio real root reduced remainder required equation Scholium Second Degree Solution Solve the equation square root subtracted tained term multiplied tity unity unknown quantity whence
Passagens conhecidas
Página 47 - 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 54 - 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 149 - Multiply the divisor, thus increased, by the last figure of the root; subtract the product from the dividend, and to the remainder bring down the next period for a new dividend.
Página 197 - Problem. To find the last term of an arithmetical progression when its first term, common difference, and number of terms are known. Solution. In this case a, r, and n are supposed to be known, and I is to be found.
Página 262 - The logarithm of any power of a number is equal to the logarithm of the number multiplied by the exponent of the power.
Página 62 - A term may be transposed from one member of an equation to the other by changing its sign.
Página 44 - Arrange the terms in the statement so that the causes shall compose one couplet, and the effects the other, putting ( ) in the place of the required term. II. If the required term be an extreme, divide the product of the means by the given extreme ; if the required farm be a mean, divide the product of the extremes by the given mean.
Página 46 - Likewise, the sum of the antecedents is to their difference, as the sum of the consequents is to their difference.
Página 99 - What fraction is that, whose numerator being doubled, and denominator increased by 7, the value becomes §; but the denominator being doubled, and the numerator increased by 2, the value becomes f?
Página 206 - The sum of the squares of the extremes of four numbers in arithmetical progression is 200, and the sum of the squares of the means is 136. What are the numbers ? Ans.
Referências a este livro
The Emergence of the American Mathematical Research Community, 1876-1900: J ... Karen Hunger Parshall,David E. Rowe Pré-visualização limitada - 1994 |