(O 
If this be not thought near enough, SubflraA this Square 
from 5*. 000000 : The Remainder 6=0.000504, divided by 
aA=4.472, or by 2 A-|-i = 4.473, gives (either way; 
0.000068 — ; which added to A = 2 236, makes 2.236068-— , 
fbmewhat too big j but 2.236067 -j- would be much more 
too licde. 
Which gives us the Square Root of adjufted to the 
fmh place of Decimal Parts, at three fteps- And by the 
fame Method, if it be thought needful, we may proceed fur- 
ther. 
It were eafie to compound the Procefs of two or more 
fteps into one, and give ( for the Rule ) the Refult of fuch 
Compofition. Which would make it feem more Intricate 
and Myfterious, to amufe the Reader : But I choofe to make 
it as plain as I can ( and therefore keep the feveral fteps fe- 
parate, ) that the Reader (for his facisfadion) may clearly 
fee the true ground of the Procefs. But of this enough. 
Proceed we now to the Cubick Root. For which (con- 
fbnanc to the Qnadratick ) the Rule is this : 
From the Non-Cnbick propofed, ( fuppsfe N, ) (ubtra<5t 
the greateft Cube in Integers therein contained, (fuppofe Ac:) 
the remainder (fiippofe B = ; A q E-}- 3 AEq+Ec^) is 
to be the Numerator of a Fraction for defigning the value of 
E, (the remaining part of the Root fought A4-E=\/cN.) 
To this Numerator, if ( for the Denominator or Divifor) 
we fubjoyn 3 A q, the Refult will certainly be too great for 
E, becaufe the Divifor is too little: (For it fliould be 
3 A q 4; 5 A E + E q, to give the true value of E. ) If, for 
the Divifor, we take 3 A q4- jA + ij it will certainly be 
too little, becaufe the Divifor is too great. ( For E, by con- 
fir udion, is lefi than i. ) It muff therefore ( between thefe 
limits ) be more than this latter. And therefore this latter 
Refiilc being added to A, will give a Root whofe Cube may 
be fabtraded from the Non-Gubick propofed, in order to 
another ftep. 
This Approach I find in Wingate's Arithmetick, Publi/hed 
in the Year 1630, and muft therefore be at leatt fo old; 
how much older I cannot tell. 
But if, for the Divifor, we take 3 A q -j- 3 A, (or even 
lefs than ) the Refuk may be too great ; or ( in cafe B be 
imall ) it may be too little, ( and oft is fo. ) 
Which 
