4 
NOTATION. 
I 
the upper part is called the numerator, and the low^r 
the denominator, as in vulgar fractions. 
The sign v' , is used to express the square root of 
any quantity to which it is prefixed: thus \/2T sig 
nifies the square root of 25 (which is 5, because 5 x 5 is 
25): thus also \/ ab denotes the square root of ab ; and 
A / ab+be . , ,, „ ab-\-bc 
y —^ .— denotes the square root of —^— or oi 
the quantity which arises by dividing ab -P be by d: 
but (because the line which separates the 
numerator from the denominator is drawn below \/ ) 
signifies that the square root of ab P be is to be first 
taken, and afterwards divided by d : so that, if a was 2, 
6 
b 6, c 4, and d 9, then would 
d 9 
•, or \/ 4, which is 2. 
1,ut v /ah d- is V— 
The same mark V, with a figure over it, is also used 
to express the cube, or biquadratic root, &c. of any 
quantity: thus \/G4 represents the cube root ot 
G4, (which is 4, because 4X4X4 is G4), and X/ab p cd 
biquadratic root of 16 (which is 2, because 2 x 2 x 2 x 
2 is 16); and X/ab p cd denotes the biquadratic root 
of ab p cd; and so of others. Quantities thus ex 
pressed are called radical quantities, or surds ; where 
of those, consisting of one term only, as v/^a~and \/ab, 
are called simple surds; and those consisting of several 
terms, or members, as y/a z — ir and V a 1 — b 2 + bc y 
compound surds.. 
Besides this way of expressing radical quantities, 
(which is chiefly followed) there are other methods 
made use of by different A uthors ; but the most com 
modious of all, and best suited to pract ice, is that where, 
the root, is designed by a vulgar fraction, placed at the. 
end of a line drawn over the quantity given. Accord-