[ 4°4 ] 
ment, or a Quantity to be added. The negative Sign 
implies a Decrement, or Quantity to be fubftraded : 
And thefe ferve to keep in our View what Elements 
enter into the Compofition of Quantities, and in 
which manner, whether as Increments or Decre- 
ments. It is the fame thing to fubftrad a Decrement 
as to add an equal Increment. As the Multiplication 
of a Quantity by a pofitive Number implies a repeated 
Addition of the Quantity, fo the Multiplication by a 
negative Number implies a repeated Subftradion : 
And hence to multiply a negative Quantity, or De- 
crement, by a negative Number, is to fubftrad the 
Decrement as often as there are Units in this Num- 
ber, and therefore is equivalent to adding the equal 
Increment the fame Number of Times 5 or, when a 
negative Quantity is multipled by a negative Number, 
the Produd is pofitive. When we inquire into the 
Proportion of Lines in Geometry, we have no regard 
to their Pofition or Form ; and there is no ground 
for imagining any other Proportion betwixt a pofitive 
and negative Quantity in Algebra, or betwixt an 
Increment and a Decrement, than that of the abfolute 
Quantities or Numbers themfelves. The Algebraic 
Expreflions, however, are chiefly ufeful, as they ferve 
to reprefent the Effeds of the Operations ; and fuch 
Expreflions are not to be fuppofed equal that involve 
equal Quantities, unlefs the Operations denoted by 
the Signs are the fame, or have the fame Effed. Nor 
is fuch Expreflion to be fuppofed to reprefent a cer- 
tain Quantity ; for if the -\/\ .1 fhould be faid to 
reprefent a certain Quantity, it muft be allowed to be 
imaginary, and yet to have a real Square i a way of 
fpeaking which it is better to avoid. It denotes only. 
