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

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Página 85

... diminished by diminishing both its terms by the same quantity ; but the

is the case , when the terms are increased instead of being diminished .

SECTION IV . Equations of the First Degree containing two or more unknown

quantities .

... diminished by diminishing both its terms by the same quantity ; but the

**reverse**is the case , when the terms are increased instead of being diminished .

SECTION IV . Equations of the First Degree containing two or more unknown

quantities .

Página 144

The preceding formula , written in the

2220–2 + & c . ( x + a ) " = x " + naza - 1 + a 2 whence it appears that The

coefficients of two terms which are equally distant , the one from the first term ,

and the ...

The preceding formula , written in the

**reverse**order of its terms , gives n ( n - 1 )2220–2 + & c . ( x + a ) " = x " + naza - 1 + a 2 whence it appears that The

coefficients of two terms which are equally distant , the one from the first term ,

and the ...

Página 148

Polynomial Theorem . are , then , obtained from those of P by derivation , while

those of Q. are obtained from those of its derivative Q " by a process , which is the

Polynomial Theorem . are , then , obtained from those of P by derivation , while

those of Q. are obtained from those of its derivative Q " by a process , which is the

**reverse**of derivation , and which , by art . 172 , consists in multiplying by q , that ... Página 231

... next term of the series , to having the

before the change the

the same sign , it introduces a permanence which is only sufficient to take the

place of ...

... next term of the series , to having the

**reverse**sign of it . Even then , if it hadbefore the change the

**reverse**sign of the preceding term and after the changethe same sign , it introduces a permanence which is only sufficient to take the

place of ...

Página 234

The

therefore , in either case , have imaginary roots . 301. Theorem . When two or

more successive terms of an equation are wanting , the equation must have ...

The

**reverse**is the case when both these terms are negative . The equation must ,therefore , in either case , have imaginary roots . 301. Theorem . When two or

more successive terms of an equation are wanting , the equation must have ...

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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...