## An Elementary Treatise on Algebra |

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3d root approximate values arithmetical mean arithmetical progression coefficient commensurable roots common difference continued fraction continued product Corollary decimals deficient terms denominator denote derivative Divide dividend divisible Elimination equal roots equation x² Examples of Equations Examples of Substitution exponent factor Find the 3d Find the 4th Find the continued Find the greatest Find the number Find the square Find the sum Geometrical Progression gives greatest common divisor Hence imaginary roots last term logarithm monomials multiplied negative roots number of permanences number of real number of terms obtained polynomial positive roots preceding article Problem quantities in example quotient radical quantities ratio reduced remainder required equation row of signs Scholium Second Degree Solution Solve the equation square root Sturm's Theorem Substitution of Unknown subtracted unity unknown quantity variable whence

### Popular passages

Page 48 - 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 127 - 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 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 192 - 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 63 - A term may be transposed from one member of an equation to the other by changing its sign.

Page 1 - ALGEBRA. CHAPTER I. FUNDAMENTAL PROCESSES OF ALGEBRA. SECTION I. Definitions and Notation. 1. Algebra, according to the usual definition, is that branch of mathematics in which the quantities considered are represented by the letters of the alphabet, and the operations to be performed upon them are indicated by signs. In this sense it would embrace almost the whole science of mathematics, elementary geometry alone being excepted. It is, consequently, subject in common use to some limitations, which...

Page 113 - The derivative of the sum of two functions is the sum of their derivatives.

Page 127 - 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.

Page 271 - The characteristic of the logarithm of a decimal fraction is a negative number* and is equal to the number of places by which its first significant figure is removed from the place of units. Thus the logarithm of...

Page 196 - Hence, to find the sum, multiply the first term by the difference between unity and that power of the ratio whose exponent is equal to the number of terms, and divide the product by the difference between unity and the ratio. Examples in Geometrical Progression. 260. Corollary. The two equations...