CHARACTERS used in .4/6rebra and Arith metic. a, 5, c, (1, &c. the first letters of the al phabet, are the characters of given quan tities; and z, y, &c. the last letters, are the characters of quantities sought. See the article ALGEBRA.
n, r, a, t, &c. are characters of inde terminate exponents both of ratios and of powers: thus, ,cm, ya, zr, &c. denote un determined powers of different kinds ; x, n y, r z, different multiples or sub multiples of the quantities x, y, z, accord ing as n, r, are either whole numbers or fractions.
± is the sign of the real existence of the quantity it stands before, and is call ed an affirmative or positive sign. It is also the mark of addition, and is read plus, or more ; thus a b, or 3+ 5, im plies a is added to 6, or 3 added to 5.
— before a single quantity is the sign of negation or negative existence, shew ing the quantity to which it is prefixed to be less than nothing. But between quan tities, it is the sign of subtraction, and is read minus, or less ; thus, a —b, or 8 — 4, implies b subtracted from a, or 8 after 4 has been subtracted.
= is the sign of equality, though Des cartes and some others use this mark x; thus, a = b signifies that a is equal to b. Wolfius and some others use the mark = for the indentity of ratios.
X is the sign of multiplication; she wing that the quantities on each side the same are to be multiplied by one another, as a x b is to be read a multiplied into b ; 4 8, the product of 4 multiplied into 8. \Collins and others make the sign of multiplication a dot between the two factors ; thus, 5. 4 signifies the product of 5 and 4. In algebra the sign is com monly omitted, and the two quantities put together; thus b d expresses the pro duct of b and d. When one or both of the factors are compounded of several letters, they are distinguished by a line drawn over them; thus, the factum of a + b into d, is wrote d X a+ b-- c,) Leibnitz, Wolfius, and others, distin guish the compound factors by including them in a parenthesis; thus (a + d.)
is the sign of division ; thus, a b denotes the quantity a to be divided by b. In algebra the quotient is often ex pressed like a fraction; thus, denotes the quotient of a divided by b. Wolfius makes the sign of division two dots ; thus, 12 : 4 denotes the quotient of 12 divided by 4 = 3. If either the divisor or divi dend, or both, be composed of several letters, for example, a b c, instead of writing the quotient like a fraction, a + b Wolfius includes the compound quantities in a parenthesis; thus, (a + : c.
(gr... is the character of involution: 4U 11 the character of evolution.
7 or c are signs of majority ; thus a 7 b expresses that a is greater than b.
L or •"M are signs of minority ; and when we would denote that a is less than b, we write a b, or a fib.
rn is the character of similitude used by Wolfius, Leibnitz, and others : it is used in other authors for the difference between two quantities, while it is un known which is the greater of the two.
:: is the mark of geometrical propor tion disjunct, and is usually placed be tween two pair of equal ratios, as 3 : 6 :: 4 : 8, shews that .3 is to 6 as 4 is to 8.
-14- the mark of geometrical proportion continued, implies the ratio to be still carried on without interruption, as, 2, 4, 8, 16, 32, 64 are in the same uninter rupted proportion.
%/ is the character of radicality, and. shews, according to the index of the power that is set over it, or after it, that the square, cube, or other root, is ex tracted, or to be extracted ; thus, V 16, or %/' 16, or V (2) 16, is the square root of 16, -Q/ 25, the cube root of 25, &c. This character sometimes affects several quantities, distinguished by a line drawn over them ' • thus V b d de dotes the sum of the square roots of b and d. When any term or terms of an equation are wanting, they are generally supplied by one or more asterisms; thus, in the equation + P +4 =O,thetcrm±py vanishing is marked with an asterism, 0 * ± 9