NOTATION, 
3 
It is likewise to be observed, that when a quantity is 
to be multiplied by itself, or raised to any power, the 
usual method of Notation is to draw a line over the 
given quantity, and at the end thereof place the Expo 
nent of the Power. Thus a-f ¿| 2 denotes the same as 
a + b x a + b, viz. the second power (or square) of 
a + b considered as one quantity: thus, also, ab -p ¿cl 3 
denotes the same as ab + bc x ab + bc x ab + bc y mz. 
the third power, (or cube) of the quantity ab + be. 
But in expressing the powers of quantities repre 
sented by single letters, the line over the top is com 
monly omitted; and so a 2 comes to signify the same 
as aa or a x a, and 6 3 the same as bbb pr b x, b x b: 
whence also it appears that a 2 i J will signify the same 
as aabbb ; and a 5 c 2 the same as aaaaacc; and so of 
others. 
The Note . (or a full point) and the word into, are 
likewise used instead of x * or as Marks of Multipli 
cation. 
Thus a + b . fl + c and a 4- b into a 4- c both signify 
the same thing as a ~f b x a c, namely, the product 
of a -f b by a -f c. 
The Sign-z-is used to signify that the quantity pre 
ceding it is to be divided by the quantity ivhich comes 
after it: Thus c -z~b signifies that c is to be divided by 
b; and a + b -z~ a — c, that a-\-b is to be divided by 
a — c. 
Also the mark ) is sometimes used as a note of Divi 
sion; thus, a -f b) ab, denotes that the quantity ab is 
to be divided by the quantity a 4- b ; and so of others. 
But the division of algebraic quantities is most com 
monly expressed by writing down the divisor under the 
dividend with a line between them (in the manner of 
a vulgar fraction). 
Thus represents the quantity 
arising by dividing c by b; 
and 
a 4- b 
a — c 
denotes the 
quantity arising by dividing a 4- b by a — c. Quantities 
thus expressed are called algebraic fractions; whereof 
jb 2