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

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Página 51

After taking away the

thirds of the original sum increased by $ 50 , or f2 + 50 . If from this sum is taken a

fourth part , there remains three fourths ; to which is to be added $ 70 , giving * ( 3

...

After taking away the

**third**part and putting in its stead $ 50 , there remains twothirds of the original sum increased by $ 50 , or f2 + 50 . If from this sum is taken a

fourth part , there remains three fourths ; to which is to be added $ 70 , giving * ( 3

...

Página 56

A

capital 2 per cent , more advantageously than the first , had an income greater by

$ 1500. Required the capitals of the three persons , and the three rates of ...

A

**third**person , who possessed $ 15 000 more than the first , and who put out hiscapital 2 per cent , more advantageously than the first , had an income greater by

$ 1500. Required the capitals of the three persons , and the three rates of ...

Página 100

In the first game A has the bank , B and C stake the

win . In the second game B has the ... After this

, and find that they have all the same sum of 64 ducats . How much had each ...

In the first game A has the bank , B and C stake the

**third**part of their money , andwin . In the second game B has the ... After this

**third**game they count their money, and find that they have all the same sum of 64 ducats . How much had each ...

Página 109

To find three numbers such that if 6 be added to the first and second , the sums

are to one another as 2 : 3 ; if 5 be added to the first and

11 ; but if 36 be subtracted from the second and

.

To find three numbers such that if 6 be added to the first and second , the sums

are to one another as 2 : 3 ; if 5 be added to the first and

**third**, the sums are as 7:11 ; but if 36 be subtracted from the second and

**third**, the remainders are as 6 : 7.

Página 159

The pound of each article costs as many dollars as there are pounds of that

article ; but he has one

3 } times as much of the

of ...

The pound of each article costs as many dollars as there are pounds of that

article ; but he has one

**third**more of the second kind than he has of the first , and3 } times as much of the

**third**as he has of the second . How many pounds has heof ...

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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...