An Elementary Treatise on Algebra: To which are Added Exponential Equations and LogarithmsJ. Munroe, 1837 - 276 páginas |
No interior do livro
Resultados 1-5 de 80
Página 14
... give it an exponent equal to the difference of its exponents in the two terms . But when a letter occurs in only one term , it is to be retained in that term , with its exponent un- changed . The required quotient is , then , equal to ...
... give it an exponent equal to the difference of its exponents in the two terms . But when a letter occurs in only one term , it is to be retained in that term , with its exponent un- changed . The required quotient is , then , equal to ...
Página 15
... give + ; unlike signs give — . EXAMPLES . 13 b 1. Divide 65 a b by 5 a . Ans . -1 2. Divide - - 132 a5 b3c by 11 a3 b3 . Ans . ― 3. Divide 144 a b3 c2 de by -112 a b c e7h . Ans . - 4. Divide - 135 by - - - 5 a . = 136 . 12 a2c . 9 cd8 ...
... give + ; unlike signs give — . EXAMPLES . 13 b 1. Divide 65 a b by 5 a . Ans . -1 2. Divide - - 132 a5 b3c by 11 a3 b3 . Ans . ― 3. Divide 144 a b3 c2 de by -112 a b c e7h . Ans . - 4. Divide - 135 by - - - 5 a . = 136 . 12 a2c . 9 cd8 ...
Página 46
... gives A : BC : D , A + C : B + D = A : B = C : D AC : B - DA : B = C : D mA + n C : m B ÷ nD = A ; B = C : D mA - n C : mB - nD - A : B = C : D ; whence AC : B + D = A — C : B — D - mA + nCm B ÷ nD = mA - n C : mB - n D ; or ...
... gives A : BC : D , A + C : B + D = A : B = C : D AC : B - DA : B = C : D mA + n C : m B ÷ nD = A ; B = C : D mA - n C : mB - nD - A : B = C : D ; whence AC : B + D = A — C : B — D - mA + nCm B ÷ nD = mA - n C : mB - n D ; or ...
Página 48
... gives A : BC : D A2 : B2 = C2 : D2 NA : NB NC : ND = Am Bm = Cm : Dm m m m m √A : √B = √C : ND A- -m B- -m = C — m : D - m . 75. Theorem . The reciprocals of two quantities are in the inverse ratio of the quantities themselves . 1 1 ...
... gives A : BC : D A2 : B2 = C2 : D2 NA : NB NC : ND = Am Bm = Cm : Dm m m m m √A : √B = √C : ND A- -m B- -m = C — m : D - m . 75. Theorem . The reciprocals of two quantities are in the inverse ratio of the quantities themselves . 1 1 ...
Página 53
... less in a page , gives the equation xy- ( x - 2 ) ( y − 3 ) = 145 . or 3x + 2y - 6 = 145 . Examples of putting Questions into Equations . 10. Three soldiers 5 * CH . III . §1 . ] PUTTING QUESTIONS INTO EQUATIONS . 53.
... less in a page , gives the equation xy- ( x - 2 ) ( y − 3 ) = 145 . or 3x + 2y - 6 = 145 . Examples of putting Questions into Equations . 10. Three soldiers 5 * CH . III . §1 . ] PUTTING QUESTIONS INTO EQUATIONS . 53.
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
2d Rem 3d root 4th root 94 become zero approximate values arithmetical progression binomial theorem coefficient commensurable roots contains the highest continued fraction continued product Corollary courier deficient terms denote dividend equal roots equal to zero 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 highest power integer last term least common multiple letter logarithm monomials number of terms obtained places of decimals polynomial Problem proportion quantities in example quotient radical quantities ratio real root reduced remainder required equation required root Scholium second term Solution Solve the equation square root substitution subtracted tained term multiplied tity unity unknown quan unknown quantity whence wine
Passagens conhecidas
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 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 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 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 203 - 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 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 1 Ans.