( 10 ) 
termedute Number. And if we chance not to hit on the 
nearefl:^ the Inconvenience will be but this, that our Leap 
will not be fo great as ocherwife it might be. Which will 
be redified by another B at the next ftep. 
« » For the Surfolide (of five Dimenfions ) we are, fromN 
(the Number propofed, being not a perfed Surfolide) to 
Subtra(5t Aqc (the greate ft Surfolide therein contained) to 
find the Remainder B=: 5- AqqE -j- lo AcEq + lo AqEc 
+ 5" AEqq-j- Eqc. Which ( as before ) if \nfe Divide by 
5Aqq, the Refult will be fbmewhat too big, (becaufe the 
Diviforis too little:) If by 5'Aqq+ioAc+ioAq+5'A4-i, 
the Refult will certainly be lefs than the true E. The juft 
value of E being fomewhat between thefe two, where we 
are to ufe our diftiretion, what Intermediate Number to take. 
Which according as it proves too great or too little, is to be 
redified at the next ftep. 
If, to dire<5i us in the choice of fuch intermediate Num- 
ber, we Ihould Multiply Rules or Precepts for fuch choice , 
the Trouble of obferving them, would be more than the 
Advantage to be gained by it. And, for the moft part, it 
will be fafe enough ( and leaft trouble) to Divide by ^Aqq, 
which gives a Quotient fomewhat too big : Which we may 
either Redifie ac Difcretion ( by taking a Number fomewhat 
iefi ) or proceed to another B, ( Affirmative or Negative, as 
the cafe fhall require J and fo onward to what exadnefi we 
pleafe. ( Which is, for fiibftance, in a manner coincident 
with Mr. Rapbfons Method, even for Affeded Equations. 
Thus, in the prefent cafe ; If the Number propofed be 
^ = 33) then is Aqc=;2, and B=;3— 32= 1 = jAqqE 
+ 10 AcEq — 10 AqEc 5: AEqq + Eqc. Which if we 
Divide by 5Aqq= 5- x = 80, the Refult 1^=0.0125', Is 
fomewhat too big for E, but not much. And if we examine 
it, by taking the Surfolide of 2.0125', or of 2^J, we fhall 
find a Negative B ( for the next ftep ) but not very confide- 
rable. Or if we think it confiderable^ we may proceed fur- 
ther to another ftep, or more than fo. 
The like Method may be applied ( and with more Advan- 
tage ) in the Higher Powers, according as the Compofition 
of each Power requires. 
And the fame Method may be of ufe ('with good Advan- 
tage) in long Numbers fif duly applied) even before we 
come 
