[ 39 ] 



DH'=HG^ + DG' =GH^ + GH%^^4^=GH^xL±i;l 

 vDH=GHx_%^ _ ^^^^ j^^ fuppofing c= i, r-c^ = a, 



\jc* -c- x' 



and c^ =b. 



DH = GH X — — - : or, the moment of the arch is equal 



M I - bx^ 



\1 I + a x^ 

 to the moment of the abfciffe multiplied into -;^=== • 



Whdrefore a curve, whofe ordinate is this latter quantity, in- 

 creafes in the fame manner as the elliptical arch ; and confe- 

 quently the area defcribed by that ordinate is analogous to 

 the length of the elliptical arch ; fo that both may be denoted 

 by the fame algebraical expreffion. 



