^34 Extenfon of Cardan’s Rule to the 
ligns + and — prefixed to them refpeclively in this fecond 
cafe as in the firft cafe. And it likewife follows that the 
odd powers of ss, to wit, ss, s 6 , s'°, s’ 4 , Sec. will alfo re- 
prefent, or be equal to, the fame powers, products, and 
multiples of the two original quantities 'f and E-, as in 
the former cafe ; but the figns + and - prefixed to the 
feveral terms reprefented by the faid odd powers of ss 
will be contrary to what they were before. 
35. If therefore in this fecond cafe of the equation 
x^—ax-r. in which - is lefs than — , we put ss - ", 
4 27 27 4 
the feries 2- — — — Sec. will reprefent, or be 
equal to, a fyftem of terms, derived from the two ori- 
ginal quantities ~ and that will be the very fame in 
point of compolition, that is, will be the very fame 
3 
powers, products, and multiples of - and 9 —, as the 
terms that were reprefented by it in the former cafe, in 
which ~ was greater than E : but the terms fo reprefent- 
ed will not all have the fame figns + and - prefixed to 
them as they had before ; but thofe terms in the faid 
fyftem, which are reprefented by the terms of the fe- 
ries 2 - — - - &x. which involve the even 
gee 243^ o$oie 
powers of ss, to wit, See. will have the fame figns 
prefixed 
