EVOLUTION BY LOGARITHMS. RULE. Divide the logarithm of the given number by the index of the power, and the number answering to the quotient will be the root required. NOTE. When the index of the logarithm is negative, and cannot be divided by the divisor without a remainder, increase the index by a number, that will render it exactly divisible, and carry the units borrowed, as so many tens to the first decimal place; and divide the rest as usual. 5. To find the second root of *093• Num. Power 093 Root 304959 Log. Here the divisor 2 is contained exactly once in the neg ative index 2, and therefore the index of the quotient Here the divisor 3 not being exactly contained in -4, 4 is augmented by 2, to make up 6, in which the divisor ' is contained just 2 times; then the 2, thus borrowed, being carried to the decimal figure 6, makes 26, which, divided by 3, gives 8, &c, END OF LOGARITHMS. ALGEBRA. DEFINITIONS AND NOTATION. 1. ALGEBRA is the art of computing by symbols. It is sometimes also called ANALYSIS; and is a general kind of arithmetic, or universal way of computation. 2. In Algebra, the given, or known, quantities are usually denoted by the first letters of the alphabet, as a, b, c, d, &c. and the unknown, or required quantities, by the last letters, as x, y, z. NOTE. The signs, or characters, explained at the be ginning of Arithmetic, have the same signification in Algebra. And a point is sometimes used for ×: thus a+b⋅ab=a+bXa-b. 3. Those quantities, before which the sign is placed, are called positive, or affirmative; and those, before which the sign -is placed, negative. And it is to be observed, that the sign of a negative quantity is never omitted, nor the sign, of an affirmative one, one, except it be a single quantity, or the first in a series of quantities, then the sign + is frequently omitted; thus a signifies the same as a, and the series a+b-c+d the same as +a+c+d; so that, if any single quantity, or if the first term in any number of terms, have not a sign before it, then it is always understood to be affirmative. 4. Like signs are either all positive, or all negative; but signs are unlike, when some are positive and others negative. 5. Single, or simple, quantities consist of one term only, as a, b, x. In multiplying simple quantities, we frequently omit the sign X, and join the letters; thus, ab signifies the same as aXb; and abc, the same as aXbXc. And these products, viz. axb, or ab, and abc, are called single or simple quantities, as well as the factors, viz. a, b, c, from which they are produced, and the same is to be observed, of the products, arising from the multiplication of any number of simple quantities. 6. If an algebraical quantity consist of two terms, it is called a binomial, as a+b; if of three terms, a trinomial, as a+b+c; if of four terms, a quadrinomial, as a+b+c +d; and if there be more terms, it is called a multinomial, or polynomial; all which are compound quantities. When a compound quantity is to be expressed as multiplied by a simple one, then we place the sign of multiplication between them, and draw a line over the compound quantity only; but when compound quantities are to be represented as multiplied together, then we draw a line over each of them, and connect them with a proper sign. Thus, a+bXc denotes that the compound quantity a+b is multiplied by the simple quantity c; so that if a were 10, b6, and c 4, then would a+bXc be 10+6×4, or 16 in to 4, which is 64; and a+bXc+d expresses-the product 、 of |