Second Cafe of the Cubick Equation x l -qx=r. 933 
| when r i~ was greater than ^ . But the figns pre- 
fixed to the faid terms will be contrary to thofe which 
were prefixed to them in the former cafe. Thus, the 
cube of — - — in the former cafe was r — — 
4 27 
3'V 
yrq 
6 4. 16 x 27 1 4 x 27X27 
- ; and the cube of q — - — in the prefent cafe 
27x27x27* 27 4 x 
is 
Zfrr 
37 
! r 4 
27x27x27 27x27x4 27X16 
, which confifts of the 
64’ 
fame terms as are contained in the cube of — - — 
4- 27 
bul 
they are placed in a contrary order to that in which they 
food in the former cafe ; and the figns that are prefixed 
to them are contrary in every term to what they were 
before. And the fame is true of all the other odd 
powers of thefe oppofite differences of y and . 
34., It follows, therefore, that if ss be put for 
in this latter cafe of the equation x‘ i -qx = r, , in which 
~ is lefs than the even powers of ss, to wit, j 4 , /, s l \ 
s' 6 , See. will reprefent, or be equal to, the fame powers, 
products, and multiples of the two original quantities 
r l~ and ~ in the prefent cafe as they reprefented in the 
former cafe, when ~ was greater, than , and ss was 
made to ftand for |1; and the feveral terms repre- 
fented by the faid even powers of ss will have the fame 
figns 
