904 Extenfion of Cardan’s Rule to the 
greater than another expreffion fomewhat different 
from the former, that fhall exhibit the true value of x 
in the fecond cafe, in which ~ is lefs than provided it 
Z 3 
be not lefs than — — , or — : and this without any men- 
2 X 27 7 54 _ ' 
tion of either impoffible, or negative, quantities. To 
fhew how this may be effected, is the delign of the fol- 
lowing pages. 
3. That the whole of this matter may be feen at one 
view, it will be convenient to fet forth the foundation 
and inveftigation of cardan’s rule for refolving the e- 
quation x 3 -qx=r, when " is greater than which may 
be done as follows. 
fhe Inveftigation of Cardan’s Rule for refolving the Cubick 
Equation x 3 *-qx=r, vohen - is greater than 
4 -27 
4. Previoufiy to the inveftigation of this rule, it will 
be proper to make the following obfervations. 
Obs, 1. In the equation x 3 -qx-r (which is apropo- 
fition affirming that x % is greater than qx, and that the 
excefs is equal to f) xx muft always be greater than q, 
and x than V q. 
Obs. 
