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

### From inside the book

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**values**of the first member 19 , 1 , 11 , 121 , 451 ; so that if there is a real root , it is probably nearly 1. Now ...**approximate**real root of the equation x3 12 x + 132 = 0 . Ans . -5,872052 . 4. Find the**approximate**real roots ... Page 242

... value of the continued fraction 1 1 2+ 3+ 2 Ans .. 2. Find the value of the continued fraction 1 1 4+ 1 3+ 2 Ans . 30 .

... value of the continued fraction 1 1 2+ 3+ 2 Ans .. 2. Find the value of the continued fraction 1 1 4+ 1 3+ 2 Ans . 30 .

**Approximate Values**of Continued Fractions . 224. Problem . To 242 [ CH . IX . ALGEBRA . Page 243

To which are Added Exponential Equations and Logarithms Benjamin Peirce.

To which are Added Exponential Equations and Logarithms Benjamin Peirce.

**Approximate Values**of Continued Fractions . 224. Problem . To find the value of an infinite con- tinued fraction . Solution . Let the fraction be 1 1 a + 1 b + c + ... Page 244

To which are Added Exponential Equations and Logarithms Benjamin Peirce.

To which are Added Exponential Equations and Logarithms Benjamin Peirce.

**Approximate Values**of Continued Fractions . 225. Theorem . The numerator of any**approximate value**, as the nth , is obtained from the numerators of the two ... Page 245

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**approximate value**, it follows that it must be true for every succeeding value . But the comparison of the values given in the preceding article shows that it is true for the third value , and therefore for every succeeding value . 226 ...### Other editions - View all

### Common terms and phrases

3d root 94 become zero approximate values arithmetical progression binomial Binomial Theorem coefficient commensurable roots common denominator continued fraction continued product Corollary courier deficient terms denote distance gone dividend equal roots equal to zero Examples of putting factor Find the 3d Find the continued Find the greatest Find the square Find the sum Free the equation gallons Geometrical Progression given equation given number gives greatest common divisor Hence imaginary roots last term least common multiple less logarithm merator monomials negative roots number of real number of terms obtained polynomial positive roots preceding article Problem proportion putting Questions quantities in example Questions into Equations quotient radical quantities ratio real root reduced remainder required equation required number Scholium Solution Solve the equation square root subtracted suppressed tained Theorem third three equations tity unity unknown quan unknown quantity whence wine

### Popular passages

Page 47 - 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.

Page 54 - 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...

Page 149 - Multiply the divisor, thus increased, by the last figure of the root; subtract the product from the dividend, and to the remainder bring down the next period for a new dividend.

Page 197 - Problem. To find the last term of an arithmetical progression when its first term, common difference, and number of terms are known. Solution. In this case a, r, and n are supposed to be known, and I is to be found.

Page 262 - The logarithm of any power of a number is equal to the logarithm of the number multiplied by the exponent of the power.

Page 62 - A term may be transposed from one member of an equation to the other by changing its sign.

Page 44 - Arrange the terms in the statement so that the causes shall compose one couplet, and the effects the other, putting ( ) in the place of the required term. II. If the required term be an extreme, divide the product of the means by the given extreme ; if the required farm be a mean, divide the product of the extremes by the given mean.

Page 46 - Likewise, the sum of the antecedents is to their difference, as the sum of the consequents is to their difference.

Page 99 - What fraction is that, whose numerator being doubled, and denominator increased by 7, the value becomes §; but the denominator being doubled, and the numerator increased by 2, the value becomes f?

Page 206 - The sum of the squares of the extremes of four numbers in arithmetical progression is 200, and the sum of the squares of the means is 136. What are the numbers ? Ans.