tie Invention of cardan’s Rules, &c. a 23' 
tity contained in them, but which (though of double the 
dimenfions of the original equations x 3 + qx—r and 
x l —qx=r, from which they were derived) will be more 
eafy to refolve than thofe equations, becaufe they will 
contain only the ftxth power and the cube of the un- 
known quantity which is their root, and confequently 
will be of the fame form as quadratic equations ; fo that 
by refolving them as quadratic equations we may obtain 
the value of the cube of the unknown quantity which is> 
their root, and afterwards, by extracting the cube-root of 
the faid value, we may obtain the value of the faid root,, 
or unknown quantity, itfeif ; and then at laft, by the re- 
lation of this laft root to x, or the root of the original 
equation, (which relation is derived from the fuppofitions 
that have been made in the courfe of the preceding tranf- 
formations) we may determine the value of x. And, if we 
pleafe to examine the feveral fteps of this procefs with 
fufficient attention, we may perceive, as we go along, that 
all thefe fubftitutions are legitimate and practicable, or 
are founded upon poffible fuppofttions ; though I can- 
not but obferve, that the writers on algebra, for the moft 
part, have not been fo kind as to fhew us that they are 
fo. But ftill the queftion recurs, “ How came scipio 
“ ferreus, of Bononia (who, as cardan tells us, was 
“ the firft inventor of thefe rules) or the other perfon, 
“ whoever- 
