NOTATION. 
5 
ing to this Notation the square root is designed by the 
fraction 4-, the cube root by 4-, and the biquadratic root 
by ¿, &c. Thus - oV expresses the same thing with 
\/a, viz. the square root of a; and a 1 4- ab] 1 the 
same as v/V + ab, that is, the cube root of a 1 + ab : 
also""a]^ denotes the square of the cube root of a ; and 
a + zl 1 ' the seventh power of the biquadratic root of 
and so of others. But it is to be observed, that, 
when the root of a quantity represented by a single 
letter is to be expressed, the line over it may be ne- 
I I T 
glected; and so a? will signify the same as a ¡“, and b* 
the same as b 1 J or \/b. The number, or fraction, by 
which the power, or root of any quantity, is thus de 
signed, is called its Index, or Exponent. " 
Th€ Marie = f called the Sign of equality J is used to 
signify that the quantities standing on each side of it are 
equal. Thus 2-\-3==5, shews that 2 more 3 is equal to 
5; and x — a — b, shews that x is .equal to the dif 
ference of a and b. 
The Note :: signifies that the quantities between which 
it stands are proportional: As a : b :: c : d, denotes 
that a is in the same proportion to b, as c is to d, or that 
if a be twice, thrice, or four times, &c. as great as b, 
then accordingly is c twice, thrice, or four times, &c. 
as great as d. 
To what has been thus far laid down on the signifi 
cation of the signs and characters used in the Alge 
braic Notation, we may add what follows; which is 
equally necessary to be understood. 
When any quantity is to be taken more than once, 
the number is to be prefixed, which shews how many 
times it is to be taken: thus 5a denotes that the quan 
tity a is to be taken five times; and 3be stands for three 
times be, or the quantity which arises by multiplying be 
by 3 : also 7v/a 2 + 6 2 signifies that s/d 1 -f h 1 is to be 
taken 7 times ; and sp of others. 
b 3