( 23*5 ) 
fo AC, then ct, will be equal to A.B, C, ( 5 :c. 
as is very evident; conlequently the Area bl the Curve 
v\hcl'e AbfcilTe is x, and Ordinate when x is = 
AC, is /"A — B -]- « X ~x C &c. that is e- 
qual to T|’* thrown into a Series, and the firll Terrn 
multiplied by A, the I'econd by B, the third by C, &c. 
But thrown into a Series, and the firll Term 
multiplied by A, the fecond by B, the third by C, 
and then the whole divided by » xw— i x«— 2, &c. 
continued to Unity, is equal to the Area of the Curve, 
whole Place in the Series is denoted by n : There- 
fore the Area of the Curve, whofe Abfcifle is 
equal to x , and its Ordinate to x” y, - taken 
when X is equal to AC, and divided by » x«~i 
X 2x«^ ^c. continued to Unity, is equal to the A- 
rea of a Curve whofe Place in the Series is denoted 
by n 5 that is, Q^, which is the Area of a Curve, 
whofe AbfcilTe is x, and Ordinate x y taken when x 
is = AC, is equal to the fecond Curve AKC; halfR, 
which is the Area to the Abfcifle x, and Ordinate 
x' y, taken in the fame manner, is equal to the third 
Curve ALC; ^^S, which is a like Area to x and x»^, 
is equal to the fourth Curve AMC ; ^ T, the Area to 
X and x^y, x being equal to AC, is equal to the fifth 
Curve ANC j and fo on perpetually (^E.D. 
< - 
VII. mris 
