( 102 ) 
you will not, without a little reflection, dif r 
cover the reafon why, when the figns of the 
multiplier and multiplicand, are different, 
you are always to prefix the negative fign 
to the product. I will endeavour to explain 
this matter. 
Pofitive and negative quantities are con r 
fidered as diametrically oppofite. If from 
a given point I draw a line to the right, I 
may call it pofitivej then a line from the 
fame point, drawn to the left, may be con- 
iidered as a negative line. Or, if I place a 
cypher in the middle and continue a line of 
figures both ways, thus 4321 o 1234, thofe 
on the right are more than nothing; thofe on 
the left I will imagine lefs. The firft may 
exprefs money which I pofTefs, the latter, 
money which I owe. Let us fuppofe, for 
example, that I find, in three different parts 
of my account-book, a debt of 15!. which 
I have borrowed of a friend. 
I exprefs it thus . . . 15: 
and finding it three time repeat- 
ed, I multiply by . . + 3 : 
that is, J tripple the debt, and 
confequently the prqduft is . 45 . 
Jf, on the contrary, I fuppofe this 15 to 
repre T 
