I 902 1 
3vLII. A Method of extending Cardan’s Rule for refohing 
one Qafe of a Cubick Equation of this Form , * - qx 
- r, to the other Cafe of the fame Equation , which it 
is not naturally fitted to folve , and which is therefore of- 
ten called the irreducible Cafe. By Francis Maferes, 
Ffq. F. R. S. Curfitor Baron of the Exchequer. 
Read July 9, 1778, 
ARTICLE I. 
I T is well known to all perfons converfant with alge- 
bra, that cardan’s rule for refolving the cubick e- 
quation x l —qx-r is only fitted to refolve it when r d is e- 
qual to, or greater than, — , or when r is equal to, or 
greater than, and that it is of no ufe in the refolu- 
tion of the other cafe of this equation, in which r is of 
any magnitude lefs than FBfl. For in this cafe - - s - be- 
y ° 3V3 + 27 
comes (according to the ufual language of algebraifts) a 
negative quantity, and confequently its fquare-root be- 
1 
comes 
