(7) 
Which comes to pais ffom hence ; becaufe E ( by Con* 
ftrudion ) is lefs than i ; and therefore 3 A E lefs than 5 A ; 
and perhaps fo much as that the addition of E q will not re« 
drefs it. And when it fo iiappens, 3 A 3 A^ is a better 
Divifor than 3 Aq + 3 A4- (or even fomev^hat lefs than 
either. ) But becaufe it doth not always fo happen ( though 
for the moft part it doth ) the Rule doth rather dired the 
other ; as which doth certainly give a Root hCs than the true 
value, whofeGube may always be fubtraded from theNon- 
Giibick propofed. The defign being to have fach a Cube as 
( being fubtraded) may leave another B, to be ordered in 
like manner for a new Approach. 
But, for the moft part, 3 A q may be fafely taken for the 
Divifor. For, though the Re&It will then be fomewhat too 
big, yet the excefs may be fo fmall, as to be negleded | or^ at 
leaft, we may thence eafily judge what Number ( fomewhat 
lefs than ic ) may be fafely taken. And if we chance to take 
it fomewhat too big, the Inconvenience will be but this, that 
B for the next ftep will be a Negative. Of which cafe wa 
lhall fpeak anon. 
Thus, for inftance ; if the Non-Cube propofed be 9 =M« 
. The greateft Integer Cube therein contained is 8 = Ac, 
( whofe Cubick Root is A = 2. ) Which Cube fubtraded , 
leaves 9 — 8 = i =B= 5 AqE-|- 3 AE q + E c. This 
divided by 3Aq = 12, gives tI = ©.083 3 3 4-> too big for E. 
But the fame divided by sAq-f- 3A-{- 1 = i2-|-64- 1=19, 
gives h = 0.0 J 26 3 -}-, too little. Or if but by 3 Aq-}- 3 A 
= 12 + 6 = 18, it gives ^1 = 5§ = o.ofjjj' yet too 
little. For the Cube of A-f- 0-06,= 2.06, is but 8.742— , 
which is fliort of 9. And fb much iliprt of it, that we oiay 
fafely take 2.07 as not too big : Or perhaps 2.08, ( which if 
it chance to be too big, it will not be much too big 5 of which 
cale we are to fpeak anon : ) And, upon tryal, it will be 
found not too big ; for the Cube of 2.08, is but 8.998912. 
If this firft ftep be not near enough : This Cube (ubtraded 
from 9.000000, leaves a new B=: 0.001 08 8, which divided 
by 3Aq=: 12.9796, gives 0.000084 — • ; which will be fome- 
what too big, but not rnuch. ( For E is now fo fmal!, as that 
3 AE may be fafely negle<5ted, and Eq much more. ) So that 
if to 2.08, we add 0.000084 — ^ the Refult 2.080084 will be 
too big, but 2.080083 will be more too little. ( As will ap- 
C 2 pear 
