(8 ) 
pear if we take the Cube of each.) So that either of them^ 
at the fecond ftep^ gives the true Root within an Unite in 
the fixth place of Etecimal Parts. 
But when I fty, Taking the Cube of each, ( which I do, that 
the thing may be more clearly apprehended) it is not necefla- 
ry that we trouble our (elves with the whole Cube. For, Ac 
being already fubtraded/or finding B=3AqE^-jA.Eq-f-Ec, 
we have no more to try, but whether j AqE-f- ;AEq-f-Ec 
be greater or lefs than Bj according as Ivc take 0.000084, 
or o.ot5oo83, for E. 
Which may conveniently be done in this manner : Take 
3 A + E, and Multiply this by E, (or E by it) fo have we 
gAE + Eq. To this add gAq, and Multiply the whole by 
{io have we gAqE + 3 AEq + Ec,) to fee whether this 
be greater or lefs than B. 
That is, in the prefent cafe, if we take E = 0.000084, 
and add to this 3 A =: 6.24, then is 6.240084= 3 A+E. 
This mulciplied by E=o.oooo84,is 3 AE^-Eq=o.oooy24^-• 
To vvhich if we add 5Aq= 12. 9792, it is 3Aq4-5AE+Eq 
= 12.979724. Which multiplied again by E = 0.000084, 
is 0.0010902 + = 3 AqE -j- 3 AEq which is more than 
B = 0.001088. 
But if we take E = 0.000083, and proceed as before, ws 
fliall have 3 AqE 3 AEq -j- Ec = 0.001077 -}-, which is 
lefs than B = 0.00108 8. And therefore (if we fubtrad that 
from this) the Remainder, o.ooooii, will be another B for 
the next fiep, if we pleafe to proceed further. 
Hitherto I have purfucd the Method moft affeded by the 
Ancients, in feeking a Square or Cube ( and the like of other 
Powers) always left than the Juft value, that it might be fub- 
traded from the Number propofed, leaving B a Pofitive Re- 
mainder ; thereby avoiding Negative Numbers. 
But fince the Arithmetick of Negatives is now fo well un- 
derltood, it may in this (and other Operations of like Na- 
ture) be advifable, to take the next greater ( in cafe that be 
nearer to the true value ) rather than the next lefler. Of 
which I took notice in my Commerctum Epi/^olicup^^ Efift. i^. 
Jan. 2. i6y|. in a cafe more intricate than this is. And 
which I ellewhere advife, in feeking the Greatefi Common Di- 
'vtfor of two Numbers, in order to the abbridging a Fradion, 
Of other wife. 
Accord- 
