C »3« ) 
The Area of the firfl Curve ADI is=A 
of the (econd A E K is = 2 : A — B 
of the third A F L 
of the fourth AGM = — 
of the fifth AHN 
and fo on perpetually. Here in ' all the Curves fol- 
lowing the firfi:, the Index of the higheft Power ol z 
is always the Number which exprefles the Diftance 
of the Curve from the firft, and afterwards decreafes 
regularly by Unity ; the firft Term is multiplied into 
A, the fecond into B, the third into C, the fourth 
into D, and fo on ; the Coefficients are the fame 
as in a Binomial raifed to the highefl: Power of z, 
and the Divifor is fo many Terms of this Progreffion 
ixax3x4x5'x^ &c as is exprefs’d by a Number 
equal to the higheft Index of z. Otherwife fuppofmg 
9/ to reprefent: the Diftance of the Curve to be mea- 
fured from the firfl: ; th en the Area fought will be 
found by extending &-- 1 I" into a Series, and multiply- 
ing the firft Term by A, the fecond by B, the third 
by C, the fourth by D, &c. and dividing the whole 
by n X n^“i x«^ continued to Unity. 
SECOND part. 
Suppofing the firfl, fecond, third, Curves to be 
the fame as before; Let t denote the whole Abfcifie 
AC, and put x for BC.* Then deferibe the Curves 
eXA, CYA, CZA, C TA, where BX fhall be e- 
qual to xy, BY=x*j, BZ = x^ y, Bf=x^y, &c. 
This being done, and in the Series of Curves CIDA, 
Hh X eXA, 
