Second Cafe of the Cubick Equation x i -qx=r. 947 
«of the impoffible binomial quantities 81+^-2700 and 
81V-2 700 is only tentative. But Mr. de moivre 
has given a certain method of finding the cube-roots of 
fuch quantities in all cafes ; but not without the trifec- 
tion of an angle, or finding (by the help of a table of 
fines, or otherwife) the cofine of the third part of a 
circular arc whofe cofine is given ; by means of which 
trifedtion it is well known (independently of cardan’s 
rule, or Mr. de moivre’s procefs) that the fecond cafe 
of the cubick equation x' — qx-r (in which E is lefs 
than 9 -\ may be refolved. So that Mr. de moivre’s 
method of doing this bufinefs, though more perfedt 
than Dr. Wallis’s, does not feem to be of much ufe in 
the refolution of thefe equations. And both methods 
are equally liable to the objection above-mentioned, of 
exhibiting to our eyes, during the whole courfe of the 
proceffes, a parcel of algebraick quantities, of which 
our underftandings cannot form any idea ; though, by 
means of the ultimate exclufion of thofe quantities, the 
refults become intelligible and true. It is by the in- 
trodudlion of fuch needlefs difficulties and myfteries in- 
to algebra (which, for the moft part, take their rife from 
the fuppofition of the exiftence of negative quantities, 
6 B a 
or 
