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

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Página 187

Sum of two Terms equally distant from the extremes . so that the nth term is

obviously 1 = a + ( n − 1 ) r . But if the series is decreasing , the

1 = a- ( n - 1 ) r . Both these cases are , however , included in one , if we suppose

r to ...

Sum of two Terms equally distant from the extremes . so that the nth term is

obviously 1 = a + ( n − 1 ) r . But if the series is decreasing , the

**last term**must be1 = a- ( n - 1 ) r . Both these cases are , however , included in one , if we suppose

r to ...

Página 190

Find the

common difference 4 , and the sum of the terms 105 . Ans . The

the number of terms = 7 . 12. Find a and n , when l , r , and S are known . 1 + fr FV

...

Find the

**last term**and number of terms of a series , of which the first term is 3 , thecommon difference 4 , and the sum of the terms 105 . Ans . The

**last term**= 27 ,the number of terms = 7 . 12. Find a and n , when l , r , and S are known . 1 + fr FV

...

Página 195

A Geometrical Progression , or a progression by quotients , is a series of terms

which increase or decrease by a constant ratio . a , l , n , and S will be used in this

section as in the last , to denote respectively the first term , the

A Geometrical Progression , or a progression by quotients , is a series of terms

which increase or decrease by a constant ratio . a , l , n , and S will be used in this

section as in the last , to denote respectively the first term , the

**last term**, the ... Página 198

To which are Added Exponential Equations and Logarithms Benjamin Peirce.

Examples in Geometrical Progression . 6. Find the ratio and sum of the series of

which the first term is 160 , the

To which are Added Exponential Equations and Logarithms Benjamin Peirce.

Examples in Geometrical Progression . 6. Find the ratio and sum of the series of

which the first term is 160 , the

**last term**38880 , and the number of terms 6 . Página 219

To which are Added Exponential Equations and Logarithms Benjamin Peirce.

Number of Imaginary Roots ; of Real Positive Roots . reduces the given first

member to its

case .

To which are Added Exponential Equations and Logarithms Benjamin Peirce.

Number of Imaginary Roots ; of Real Positive Roots . reduces the given first

member to its

**last term**, m , and this result is therefore negative in the presentcase .

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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...