nm A Conjecture concerning 
books that treat of them were firft difcovered. This we 
are fometimes enabled to do by the authors themfelves 
to whom we are indebted for thefe difcoveries, who have 
candidly informed their readers of the feveral fteps, and 
fometimes of the accidents, by which they have been led 
to them : but it alfo often happens, that the authors of thefe 
difcoveries have negledted to give their readers this fatif- 
fadtion, and have contented themfelves with either 
barely delivering the proportions they have found out, 
without any demonftrations, or with giving formal and 
pofitive demonftrations of them, which command indeed 
the aifent of the underftanding to their truth, but afford 
no clue whereby to difcover the train of reafoning by 
which they were firft: found out; and confequently con- 
tribute but little to enable the reader to make fimilar dif- 
coveries himfelf on the like fubjedfs. This feems to be the 
cafe with thofe ingenious rules for the refolution of cer- 
tain cubic equations, which are ufualiy inown by the 
name of cardan’s rules. We are told to make certain 
fubftitutions of feme quantities for others in thefe equa- 
tions x^+qx-r and xl—qx^r (which are the objects of 
thofe rules) and certain fuppofitions concerning the 
quantities fo fubftituted ; by doing which we find, that 
thofe equations will be transformed into other equations 
which will involve the fixth power of the unknown quan- 
tity 
