l\o JSiifcettanea, Cur i of a* 



Jl- Method of Squaring fome forts 

 of Curves, or Reducing them 

 to more fimfle Curves. 



By 4 De Moivre, &S.S. 



IT E T A be the Area of a Curve, whofe 

 1 j Abiciife is and Ordinate Applicate 



x V dx — xx. Let B be the Area of a Curve, 

 whofe Abfcifle is the fame with the former, 



m— - n y- — ■ 



and its Ordinate x -ydx~ xx. Put 



V dx ~ xx == ^. Then will A = ^ B into 



-— r- into — t- into — ~ into - — '&c.=P 



2m^j-4 2m-j-2 2m ' 2m— 2 ! 



1 m— 1 , 



. 2W4-I m — 2 , 



— — t~ into — 1— a: • ■ y 3 =2 — R 



d 2 . 2m-W . 2 m — 1 — 2 _ 



— into —7- uito * y ' s — S 



. 2m-hi . 2m— -1 . 2m — 3 



- into — r— into —ft into 



- m-i xuw/ 2m^4 ' 2m+2 

 *^j 3 «*T t &c. 



Where we are to Note, 1. That n is fup- 

 pos'd to be an Integer and Affirmative, 

 Number. 2. That the Quantity d*B r in the 



Series 



