An Elementary Treatise on Algebra: To which are Added Exponential Equations and Logarithms |
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Página 26
Terms of a fraction may be multiplied or divided by the same quantity . CHAPTER
II . FRACTIONS AND PROPORTIONS . SECTION I. Reduction of Fractions . 54.
When a quotient is expressed by placing the dividend over the divisor with a line
...
Terms of a fraction may be multiplied or divided by the same quantity . CHAPTER
II . FRACTIONS AND PROPORTIONS . SECTION I. Reduction of Fractions . 54.
When a quotient is expressed by placing the dividend over the divisor with a line
...
Página 39
Sum and Difference of Fractions . 2 a 3 b c 5. Reduce to one fraction the
expression + c . a + bc Ans . b 5df beg 6. Reduce to one fraction + 8 62c 6 62 c2
16 abct 15 cdf - 4beg Ans . 24 62 c2 1 7. Reduce to one fraction + 22 23 ° ax - b2
+ 1 Ans ...
Sum and Difference of Fractions . 2 a 3 b c 5. Reduce to one fraction the
expression + c . a + bc Ans . b 5df beg 6. Reduce to one fraction + 8 62c 6 62 c2
16 abct 15 cdf - 4beg Ans . 24 62 c2 1 7. Reduce to one fraction + 22 23 ° ax - b2
+ 1 Ans ...
Página 42
Now a fraction is multiplied either by multiplying its numerator or by dividing its
denominator ; and it is divided either by ... Hence , It has the same effect to
multiply one of the terms of a fraction by a quantity , which it has to multiply the
other term ...
Now a fraction is multiplied either by multiplying its numerator or by dividing its
denominator ; and it is divided either by ... Hence , It has the same effect to
multiply one of the terms of a fraction by a quantity , which it has to multiply the
other term ...
Página 248
Value of Continued Fractions . CHAPTER IX . CONTINUED FRACTIONS . 316. A
continued fraction is one whose numerator is unity , and its denominator an
integer increased by a fraction , whose numerator is likewise unity , and which
may ...
Value of Continued Fractions . CHAPTER IX . CONTINUED FRACTIONS . 316. A
continued fraction is one whose numerator is unity , and its denominator an
integer increased by a fraction , whose numerator is likewise unity , and which
may ...
Página 256
Approximate Values of Fraction or Ratio . and the required continued fraction is 1
= 2+ 1 1+ 1 2+ - 1 itor 326. Corollary . The values of a ' , a " , & -c . , in the case of
a vulgar fraction , are evidently the quotients which would be obtained by the ...
Approximate Values of Fraction or Ratio . and the required continued fraction is 1
= 2+ 1 1+ 1 2+ - 1 itor 326. Corollary . The values of a ' , a " , & -c . , in the case of
a vulgar fraction , are evidently the quotients which would be obtained by the ...
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An Elementary Treatise on Algebra: To which are Added Exponential Equations ... Benjamin Peirce Visualização integral - 1842 |
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 |
Palavras e frases frequentes
affected approximate values arithmetical becomes body called coefficient consequently contained continued fraction continued product Corollary corresponding decimal denominator denote derivative difference Divide dividend division Elimination equal roots equation 23 EXAMPLES exponent expression Extract factor figure Find Find the greatest Find the square Find the sum follows fourth fraction Free function gallons given equation gives greater greatest common divisor Hence imaginary increased infinite integral known last term least less letter limit logarithm means method monomials multiplied negative number of real number of terms obtained places polynomial positive Problem progression Proof proportion putting quotient ratio real roots reduced remainder result reverse row of signs Solution Solve the equation square root substitution subtracted successive suppressed Theorem third true unity unknown quantity variable whence wine
Passagens conhecidas
Página 46 - 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 190 - 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 266 - The logarithm of the quotient is equal to the logarithm of the dividend, diminished by the logarithm of the divisor.
Página 61 - A term may be transposed from one member of an equation to the other by changing its sign.
Página 184 - I = the last term, r = the common difference, n = the number of terms, S = the sum of all 'the terms.
Página 53 - 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 30 - 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 125 - 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 230 - 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 45 - 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...