i*yi jMifcettanea Curiofa. 



aE% 2# — 9 



4 f-* + &c. 



n~ 5 



la this Infinite Series, thefe things are to 

 Be taken notice ofY(i.) That the Capital 

 Letters A, B, C, D, E, &c. denote the Co- 

 efficients of the Terms immediately pre- 



inraa -\~ raa 



■ ceeding them, viz.. A == - — — — — B =jjf 



ajytin — i aB*in — 3 • 



— - — >— * — 7 C == i >— — j and fo on. (2.) 



n — 1 2 

 That if the Exponent n be an Integer and 

 Pofitive, or equal to nothing, or if in be art 

 odd Number, then the Quadrature of the 

 Space ABD may be exhibited by a finite 

 Quantity: The Series in thefe Cafes breaking 

 off*. (3.) That q denotes the Term la ft break- 

 ing offT (4.) That all thofe Figures in which 

 the Series is broke off have one Geometri- 

 cally Quadrable Portion very eafily afllgn- 

 able from the Series it felf, viz.ii you make 



the AbfcifTe y = r n '\" 1 -J- nq-\-q n 'V l ; there 

 will arife a Geometrically Quadrable Area an* 

 fvvering to this AbfcifTe. (5.) That only the 



Irrational Terms \J zay—yy is to be multi- 

 tiplied into the Terms following it. 



Example 



