An Elementary Treatise on Algebra: To which are Added Exponential Equations and LogarithmsJ. Munroe, 1843 - 284 páginas |
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Página 15
... dividend is equal to its exponent in the divisor , when , for instance , am is to be divided by am , the exponent of the letter in the Exponent equal to Zero . Negative Exponents . quotient becomes CH . I. § V. ] 15 . DIVISION .
... dividend is equal to its exponent in the divisor , when , for instance , am is to be divided by am , the exponent of the letter in the Exponent equal to Zero . Negative Exponents . quotient becomes CH . I. § V. ] 15 . DIVISION .
Página 16
... becomes zero . But the quotient of a quantity di- vided by itself is unity . Whence any quantity with an exponent equal to zero is unity . Thus , am amao 1 . = 38. Corollary . When , in example 6 of art . 30 , the ex - 6 ponent n of a ...
... becomes zero . But the quotient of a quantity di- vided by itself is unity . Whence any quantity with an exponent equal to zero is unity . Thus , am amao 1 . = 38. Corollary . When , in example 6 of art . 30 , the ex - 6 ponent n of a ...
Página 23
... becomes equal to an − 1 , which gives the peculiar result an - an a = nan - 1 - a 52. There are sometimes two or more terms in the divisor , or in the dividend , or in both , which contain the same highest power of the letter accord ...
... becomes equal to an − 1 , which gives the peculiar result an - an a = nan - 1 - a 52. There are sometimes two or more terms in the divisor , or in the dividend , or in both , which contain the same highest power of the letter accord ...
Página 33
... become . 3 a x7 3 a2 x6 24 a5 x3 . - - 2 b2 c x4—2 a b2 c x3 + 4 a2 b2 c x2 — 6 a3 b2 c x - 20 a1 b2 c . The greatest common divisor of these two quantities , found as in the preceding example , is x - 2 a , which , mul- tiplied by the ...
... become . 3 a x7 3 a2 x6 24 a5 x3 . - - 2 b2 c x4—2 a b2 c x3 + 4 a2 b2 c x2 — 6 a3 b2 c x - 20 a1 b2 c . The greatest common divisor of these two quantities , found as in the preceding example , is x - 2 a , which , mul- tiplied by the ...
Página 34
... become 4 3 · 3 x2 | y2 + 2 x2 | y 3 y2 + 2x2 + 8x 6 + 9x x | y1 . x2 - 3 3 3 + 2 2 2 - and 93 . - 3 x y2 +2 - -4 xy + 4x . 6 x ། ཙ The suppression of the factor ( x - 3 ) y in the first of these polynomials reduces it to y3-2xy2-3xy + ...
... become 4 3 · 3 x2 | y2 + 2 x2 | y 3 y2 + 2x2 + 8x 6 + 9x x | y1 . x2 - 3 3 3 + 2 2 2 - and 93 . - 3 x y2 +2 - -4 xy + 4x . 6 x ། ཙ The suppression of the factor ( x - 3 ) y in the first of these polynomials reduces it to y3-2xy2-3xy + ...
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
126 become zero 3d root arithmetical progression 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 proportion 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 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 186 - I = the last term, r = the common difference, n = the number of terms, S = the sum of all 'the terms.
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 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 127 - Subtract the square of the root from the first period, and to the remainder bring down the second period for a dividend. III. Double the root already found and place it on the left for a divisor.
Página 232 - Rule. 324. An equation of any degree whatever cannot have a greater number of positive roots than there are variations in the signs of Us terms, nor a greater number of negative roots than there are permanences of these signs.
Página 47 - Likewise, the sum of the antecedents is to their difference, as the sum of the consequents is to their difference. Ratio of Sum of two first Terms to that of two last. Moreover, in finding...