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

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Página 2

Thus 3 x 5 x 7 , or 3.5.7 is the

xb , or 12.a.b , or 12 ab , is the

a product is sometimes called its coefficient , and the numerical factor is called ...

Thus 3 x 5 x 7 , or 3.5.7 is the

**continued product**of 3 , 5 , and 7. Likewise 12 x axb , or 12.a.b , or 12 ab , is the

**continued product**of 12 , a , and b . 5. The factor ofa product is sometimes called its coefficient , and the numerical factor is called ...

Página 10

But , as the order of the factors may be changed at pleasure , the numerical

factors may all be united in one product . Hence the coefficient of the product ...

Find the

am by ...

But , as the order of the factors may be changed at pleasure , the numerical

factors may all be united in one product . Hence the coefficient of the product ...

Find the

**continued product**of 3 a 6,2 cd , and e f g . Ans . 6 abcdefg . 3. Multiplyam by ...

Página 12

... product of -a , –a , –a , and Ans . a4 . 9. Find the

c e , -a , -eza , c , - 2 az , -3 abex , -7 , and 13 x3 . Ans . 42 a5 65 c3 e5 27 . 10.

Find the

.

... product of -a , –a , –a , and Ans . a4 . 9. Find the

**continued product**of — alb ,c e , -a , -eza , c , - 2 az , -3 abex , -7 , and 13 x3 . Ans . 42 a5 65 c3 e5 27 . 10.

Find the

**continued product**of 7 abi , - az , - I , 62x7 , -26 , — 3 , and — 5 a7 63 25.

Página 40

Product and Quotient of Fractions . of two quantities is equal to the greater of the

two quantities ; and that the difference of half ... The

fractions is a fraction the numerator of which is the

...

Product and Quotient of Fractions . of two quantities is equal to the greater of the

two quantities ; and that the difference of half ... The

**continued product**of givenfractions is a fraction the numerator of which is the

**continued product**of the given...

Página 277

To which are Added Exponential Equations and Logarithms Benjamin Peirce.

Involution by Logarithms . 28. EXAMPLES . 1. Find the

78.052 , 0 · 6178 , 341000 , 100-008 , and 0-0009 . Solution . We find , from the

tables ...

To which are Added Exponential Equations and Logarithms Benjamin Peirce.

Involution by Logarithms . 28. EXAMPLES . 1. Find the

**continued product**of78.052 , 0 · 6178 , 341000 , 100-008 , and 0-0009 . Solution . We find , from the

tables ...

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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...