C *35 ) 
Demnfiration of the Second Part. 
Suppofe any Curve whofe Diflance from the firft is 
denoted by n i then the Curve whofe Abfcifle is BC or 
A-, and its Ordinate divided by nxn'^ x 
&c. continu’d to Unity will be equal to it, when x is 
equal to AC or t. 
It is evident, that when the Areas ABD, ABO, 
ABP, ABQ, ABR, &c. decreafe, the Areas BCID, 
BCSO, BCTP, BCVQ^, BCWR increafe refpedive- 
ly; and confequently the Decrements of the Areas 
ABD, ABO, ABP, or their Fluxions with a ne-- 
gative Sign, are the Increments or Fluxions of the 
Areas BCID, BCSO, BCTP, &c. that is, calling the A- 
rea BCID, « ; the Area BCSO, ; the Area BCTP, y; 
Bcva,«^> BCWR, g : then 
• • • 
-*-i, «= — s. 
Now the Fluxion of the Curve, wdiofe AbfcifTe is 
= or BC,' and its Ordinate =^x’'y is x ; that 
is, equal to i y x j x being =t — z ; or fince 
the Increment of or x is equal to the Decrement 
of Zy or — the Fluxion of the fame Curve is e- 
W— I 
qual to — t — in r « x z + ” ^ ~ 
X 2 ^ &C. z y-|- n zzy — « x~^ 2 2^^, &c. 
that is, = /’* X — a — n ^”"^x — i 4- « x-7 x — c, 6(c* 
or = r « — + &c. and taking 
I'the' Fhiefits, the Area of the Curve, whofe Abfcille 
isxjor BC,and Ordinate at” is equal to /2 
8cc. But when x is equal 
to 
