g 20 Extenfion of Cardan’s Rule to the 
19. Note. The foregoing method of refolving the 
cubicle equation x^-qx-r, when r is greater than 
or “ greater than and a like method of refolving 
the cubicle equation x l + qx -r (which holds good in all 
cafes, whatever be the magnitudes of q and r), are ufu- 
ally known by the name 6f cardan’s rules, becaufe 
they were firft publifhed by him in his treatife of alge- 
bra, intitled, Ars magna, quant vulgb Cojfam vocant, feu 
regulas Algebraicas , in the year 1545, although, as he 
himfelf informs us, they were firil found out by one 
scipio FERREUS of Bononia. See wallis’s algebra, 
Chap. XIII. 
Of the fecond cafe, of the cubiek equatiqn 'x-qx~r ; in 
which r is lets than 2 lfl 0 r - is lets than — , and which 
J 3 V) ’ 4 -7 
cannot be refolved by cardan’s rule. 
, NJ- 
20. The remaining cafe of the cubicle equation a 3 - 
qx-r , in which r is lefs than — fX or - is lefs than -» 
3 V 3 4 27 
and which confequently cannot be refolved by the rules 
above-mentioned, has, upon that account, obtained a- 
mongft algebraifts the name of the irreducible cafe: at 
lead; it is often called by thq French writers of algebra 
le cas irreducible. The objedt of the remaining pages 
of 
