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

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Página 14

Since the

obtained by suppressing in the

explicitly contained in the

...

Since the

**dividend**is the product of the divisor and quotient , the quotient must beobtained by suppressing in the

**dividend**all the factors of the divisor which areexplicitly contained in the

**dividend**, and simply indicating the division with regard...

Página 18

The term of the

the product of the term of the divisor which contains the highest power of the

same letter , multiplied by the term of the quotient which contains the highest

power ...

The term of the

**dividend**, which contains the highest power of any letter , must bethe product of the term of the divisor which contains the highest power of the

same letter , multiplied by the term of the quotient which contains the highest

power ...

Página 19

In the following solution the

powers of the letter x ; the divisor is placed at the right of the

quotient below it . As each term of the quotient is obtained , its product by the

divisor ...

In the following solution the

**dividend**and divisor are arranged according to thepowers of the letter x ; the divisor is placed at the right of the

**dividend**with thequotient below it . As each term of the quotient is obtained , its product by the

divisor ...

Página 127

Double the root for a divisor , and the quotient of the

hand figure , divided by the divisor , is the next figure of the required root ; which

figure is also to be placed at the right of the divisor . Multiply the divisor , thus ...

Double the root for a divisor , and the quotient of the

**dividend**exclusive of its righthand figure , divided by the divisor , is the next figure of the required root ; which

figure is also to be placed at the right of the divisor . Multiply the divisor , thus ...

Página 280

Subtract the logarithm of the divisor from that of the

which the remainder is the logarithm , is , by art . 13 , the required quotient . Or ,

since , by art . 81 , multiplying by the reciprocal of a number is the same as ...

Subtract the logarithm of the divisor from that of the

**dividend**, and the number , ofwhich the remainder is the logarithm , is , by art . 13 , the required quotient . Or ,

since , by art . 81 , multiplying by the reciprocal of a number is the same as ...

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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...