## An Elementary Treatise on Algebra: To which are Added Exponential Equations and Logarithms |

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Página 73

A

other 5. He wishes to mix both

have 50 gallons , and each gallon , without profit or loss , may be sold for 8 ...

A

**wine**merchant has two kinds of**wine**; the one costs 9 shillings per gallon , theother 5. He wishes to mix both

**wines**together , in such quantities , that he mayhave 50 gallons , and each gallon , without profit or loss , may be sold for 8 ...

Página 76

Ans . When either a = c , or b = c ; and , in either case , these equations indicate

that the price of one of the

course , needs none of the other

and ...

Ans . When either a = c , or b = c ; and , in either case , these equations indicate

that the price of one of the

**wines**is just that of the required mixture , and , ofcourse , needs none of the other

**wine**added to it to make it of the required value ;and ...

Página 83

When a < c ; that is , when the price of the most expensive

of the required mixture . ... case the problem is altogether impossible , for two

either of ...

When a < c ; that is , when the price of the most expensive

**wine**is less than thatof the required mixture . ... case the problem is altogether impossible , for two

**wines**cannot be mixed together so as to produce a**wine**more valuable thaneither of ...

Página 93

A person had two barrels , and a certain quantity of

obtain an equal quantity in each , he poured out as much of the first cask into the

second , as the second already contained ; then , again , he poured out as much

of ...

A person had two barrels , and a certain quantity of

**wine**in each . In order toobtain an equal quantity in each , he poured out as much of the first cask into the

second , as the second already contained ; then , again , he poured out as much

of ...

Página 99

What fraction is that , whose numerator being doubled , and denominator

increased by 7 , the value becomes ş ; but the denominator being doubled , and

the numerator increased by 2 , the value becomes ? Ans .. 9. A

has two ...

What fraction is that , whose numerator being doubled , and denominator

increased by 7 , the value becomes ş ; but the denominator being doubled , and

the numerator increased by 2 , the value becomes ? Ans .. 9. A

**wine**merchanthas two ...

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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...