reprefent all the guineas in my purfe, I 
write it thus . . . +15- 
But I owe 3 times 15 guineas; I 
therefore prefix the negative fign 3. 
And the product is 45, 
as before: 
Now fuppofing the letter a to ftand for 15 
guineas, the real ftate of my account may 
be thus algebraically represented . . . 
a 3#= 30. That is, I am 30 guineas 
worfe than nothing. In both cafes the pro- 
priety of prefixing the negative fign is evi- 
dent, becaufe the product is really a defect. 
In multiplying a negative quantity, or defi- 
ciency, or debt, I am adding it to itfelf as 
often as there are units in the multiplier. I 
thus increafe the debt, but I do not thereby 
alter its nature: it flill remains a debt, and 
therefore retains its negative fign. To un- 
derftand the other cafe, viz. when a pofitive 
quantity is multiplied by a negative, it is 
neceflary to recollect, that to multiply my 
debts, is in fact, to fubtract from my real 
fubftancej therefore, though I work by 
multiplication, when the multiplier has the 
negative fign, I am actually fubtracting the 
multiplicand from reality; that is, reducing 
Q 4 it 
