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

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An Elementary Treatise on Algebra to Which Are Added Exponential Ewquations ... Benjamin Peirce No preview available - 2019 |

### Common terms and phrases

126 become zero 3d root arithmetical progression Binomial Binomial Theorem coefficient commensurable roots common difference contained continued fraction continued product Corollary deficient terms denote derivative Divide dividend division equal roots equal to zero factor Find the 3d Find the 4th Find the continued Find the greatest Find the number Find the square Find the sum Free the equation Geometrical Progression given equation given number gives greatest common divisor Hence imaginary roots last term least common multiple letter logarithm monomials multiplied number of real number of terms polynomial positive roots preceding article Problem quantities in example quotient radical quantities ratio real roots reduced remainder required equation required number row of signs Scholium Second Degree Solution Solve the equation square root Sturm's Theorem subtracted Theorem unity unknown quantity variable whence

### Popular passages

Page 55 - 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 125 - 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 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.

Page 266 - The logarithm of the quotient is equal to the logarithm of the dividend, diminished by the logarithm of the divisor.

Page 266 - The logarithm of any power of a number is equal to the logarithm of the number multiplied by the exponent of the power.

Page 63 - A term may be transposed from one member of an equation to the other by changing its sign.

Page 32 - 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 ; th<s remainder of the division is the 4th line of col.

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 1 Ans.

Page 113 - The derivative of the sum of two functions is the sum of their derivatives. Proof. Let the two functions be u and ». and let their values, arising from an infinitesimal change i in the value of their variable, be «' and v'; the increase of their sum will be («, + »') -(« + ») or «' U -\- V > V, and therefore the derivative of the sum is u' — uv, — v -T I ' i which is obviously the sum of their derivatives.

Page 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.