[ 2 46 ] 
It is not neceffary, that the curve fhould be de- 
fcribed with accuracy, or even that it fhould fall upon 
the plane or frame, except where it erodes or attempts 
to crofs the bafe ; and therefore there will arife no 
inconveniency in this refpedt from taking the lines 
OA, AB, &c. large. But the immoveable rQlers 
OD and T c mud be fixed fo near together, that, 
their diftance D c or OT, being reckoned unity, the 
bafe OT extended to the extremity of the plane to 
the right, may take in all the affirmative roots : and 
when extended to the left, may take in all the nega- 
tive ones. 
There is one thing more, very well worth obferv- 
ing, viz. that if you have an equation of this fort 
xxx — $xx-\- izoox-f- 9000 = 0 (where you may ob- 
ferve, that the coefficients unity, 5,1200 and 9000 
are fo very different from each other, that it would 
be difficult to fet them off in due proportion upon 
the line OD) you may reduce them into a more 
manageable form, by the following contrivance: in- 
ftead of each x in the equation put iox, 2 ox or 
ioox , fuppofe 20 x then indead of xxx you will 
have 8oooxxx, inflead of — $xx you will have 
— 2oooxx, &c. and the whole equation will dand 
thus, 8000 xxx — 2000 xxx -f 24000 x 4- 9000 = 0 ; 
then divide each term by 100, and you bring it to 
Sxxx — 2**4- 24* 4 - 9 = 0, a much more tradfable 
equation than the other : but then it mud be remem- 
bered, that as you made x 20 times lefs than it was, 
the roots when dilcovered will be fo many times lefs 
than the true ones, and therefore each mud be mul- 
tiplied by that number 20. 
The 
