An Elementary Treatise on Algebra: To which are Added Exponential Equations and LogarithmsJ. Munroe, 1837 - 276 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 x y , 1 may be regarded 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 x y , 1 may be regarded 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 a5 , and the exponent of a may be regarded as 1 . 7. The root of a quantity is the quantity which , multiplied a certain number of times by itself , pro- duces the given quantity ; and the ...
... unity . Thus the fifth power of a is written a5 , and the exponent of a may be regarded as 1 . 7. The root of a quantity is the quantity which , multiplied a certain number of times by itself , pro- duces the given quantity ; and the ...
Página 14
... unity , the quotient is simply equal to the remaining portion of the divi- dend . The sign of the quotient must , from art . 26 , be the same as that of the divisor when the dividend is positive , and it must be the reverse of that of ...
... unity , the quotient is simply equal to the remaining portion of the divi- dend . The sign of the quotient must , from art . 26 , be the same as that of the divisor when the dividend is positive , and it must be the reverse of that of ...
Página 16
... unity . Whence any quantity with an exponent equal to zero is unity . Thus , am am a = 1 . 32. Corollary . When , in example 6 of art . 30 , the expo- nent 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 , am am a = 1 . 32. Corollary . When , in example 6 of art . 30 , the expo- nent n of a in the divisor is greater than its exponent m in the dividend , the ...
Página 28
... unity , the given quantities have no common divisor , and are said to be incommensurable or prime to each other . EXAMPLES . 1. Find the greatest common divisor of 1825 and 1995 . Solution . 1995 | 1825 1825 1 1825 170 , 1st Rem . 1700 ...
... unity , the given quantities have no common divisor , and are said to be incommensurable or prime to each other . EXAMPLES . 1. Find the greatest common divisor of 1825 and 1995 . Solution . 1995 | 1825 1825 1 1825 170 , 1st Rem . 1700 ...
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.