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

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Página 226

Number of Real Roots . and in this case the

that when r = -00 is , - , + , - ; so that the two different roots of the equation are , in

this case , real . The

Number of Real Roots . and in this case the

**row of signs**when x = 0 is +++ ; andthat when r = -00 is , - , + , - ; so that the two different roots of the equation are , in

this case , real . The

**row of signs**when . x = l is ( like b ) , - F ( unlike b ) ; so that ... Página 229

To which are Added Exponential Equations and Logarithms Benjamin Peirce.

Number of Real Roots . co it is in which case , the

tet ; when x =- , + , - , ti 80 that the equation has three real roots ; the

...

To which are Added Exponential Equations and Logarithms Benjamin Peirce.

Number of Real Roots . co it is in which case , the

**row of signs**when a = co is tot ,tet ; when x =- , + , - , ti 80 that the equation has three real roots ; the

**row of signs**...

Página 231

Find the

value р of the variable , and also for a value 9 of the variable . The number of real

roots of the equation , comprised between p and q , cannot be greater than the ...

Find the

**row of signs**corresponding to the values of U , U , U ' , U " , & c . , for anyvalue р of the variable , and also for a value 9 of the variable . The number of real

roots of the equation , comprised between p and q , cannot be greater than the ...

Página 232

A complete equation cannot have a greater number of positive roots than there

are variations in the

roots than there are permanences in this

that of ...

A complete equation cannot have a greater number of positive roots than there

are variations in the

**row of signs**of its terms , nor a greater number of positiveroots than there are permanences in this

**row of signs**. Proof . If the equation isthat of ...

Página 239

Sturm's theorem gives = 5 23 - 6 x + 2 U = 15 22 6 U ' = 2 x 1 U " = 3 ; so that the

three real roots . The

...

Sturm's theorem gives = 5 23 - 6 x + 2 U = 15 22 6 U ' = 2 x 1 U " = 3 ; so that the

**row of signs**when x = 4 is tot , titi when = 4 it is - , + - , + ; so that the equation hasthree real roots . The

**row of signs**when x = 0 is + , - , - , + ; so that two of the roots...

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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...