■224 -A Conjecture concerning 
■“ whoever he was, that invented them, to think of mak- 
“ ing thefe lucky fubftitutions which thus transform the 
“ original cubic equations into equations of the lixth 
“ power which contain only the fixth and third powers 
“ of the unknown quantities which are their roots, and 
“ confequently are of the form of quadratic equations ?” 
To anfwer this queftion as well as I can by conje&ure 
(for I know of no hiftorical account of this matter in 
any book of algebra) and in a manner that appears to 
me to be probable , is the delign of the following pages. 
2. The moft probable conjecture concerning the in- 
vention of thefe rules, called cardan’s rules, by scipio 
ferreus, of Bononia, or whoever elfe was the inventor 
of them, feems to be this: that the faid inventor tried a 
great variety of methods of reducing the three cubic 
equations of the third clafs, to wit, x z +qx = r and 
ft 
x 3 -qx~r, and qx-x' i —r (to fome one of which all other 
cubic equations may, by proper fubftitutions, be reduced) 
to a lower degree, or to a more fimple form, by fubfti- 
tuting various quantities in the ftead of x, in hopes that 
fome of the terms arifing by fuch fubftitutions might be 
equal to others of them, and, having contrary figns pre- 
fixed to them, might deftroy them, and thereby render 
the new equation more fimple and manageable than the 
old one. And, amongft other trials, it feems natural to 
y imagine, 
