(9) 
According to this Notion^ for the Square Root of I 
would fay, it is ( 2 + ) fomewhat more than 2 ; and enquire^i 
How much more ? But for the Square Root of 8, I would 
fay, it is (5 — ) fomewhat lefi than 3 5 and inquire. How 
much left? Taking (in both cafes) that which is neareft to 
the juft Value. 
Thus, in the Cubick Root before us ; I would take for E 
C in the laft Enquiry ) 0.000084 ( where , for the next 
ftep, we haveB = — 0.000002^) rather than 0.0000834^ 
(where, for the next ftep, we fliould have B = -1-0.000011.;) 
In the latter cafe, we are to Divide 6= + 0.00001 1, by 
3Aq = i2.98o236 — , to find (by the (Quotient) how much 
is to be added to 0.00008 j. In the other cafe, we are to 
Divide B = -{- 0.000002, by ;Aq = 12 980248, to find (by 
the Quotient) what is to be abated of 0.000084. So have we 
O.QOOOI I 
12.98025^ ~ 0.00000085"+ to be added to 6.240083 : Or 
— 0.000002 ' ^ 
" 12 98 0248 ~ o-ooooooi y + to be abated of 6.240084. (Or 
it may fuffice, in eicher, to Divide by 12 98+, or even by 
13.—, without being incumbred with a long Divifbr) ei- 
ther of which gives us, for the Root fought, 2.0800838^ 
proxime. True ( at the third ftep ) to the Eighth place of De- 
cimal Parts. And if this be not near enough, the Cube of 
this, compared with the Number propofed, will give us ano- 
ther B for the next ftep. And fo onwards as far as we 
pleafe. 
Now, what is fald of the Cube, is eafily applicable to the 
Higher Powers. 
I (hall omit that of the Biqaadrate ; becaufe here perhaps 
it may be thought moft advifable, to Extrad the Square Root 
of the Number propofed 5 and then the Square Root of that 
Root. 
But if we would do it at once, we are from N ( the Num- 
ber propofed, being not a Biquadrate) to Subtrad Aqq (the 
greateft Biquadrate contained in it ) to find the Remainder 
B=4AcE + 6AqEq + 4 AEe + Eqq; Which Remainder, 
if we Divide by 4 Ac, the Quotient will certainly be too big 
for E,Cthough perhaps not much:) If by 4 Ac+6Aq+4A+i, 
it will certainly be too little ( for reafons before mentioned.) 
And we are to ufe our diicretlon in taking fome in- 
termediate 
