Mifcellanea Curiofa. 257 



ABD - % — ~ + V lay + y»* — £ — 



— + — . And if you take y s= \/f ^ 



there will arife a Geometrically Quadrable 

 Area fitting this Abfciffe, viz. Area = r% 



I have other Theorems of this Mature, 

 for Figures depending on the Circle and Pa- 

 rabola ^ but thefe two may fuffice as a Spe- 

 cimen to fhew the Ufe of my Method pub- 

 lifli'd in my Treatife of Quadratures, in de- 

 termining the Quadratures of Irrational Fi- 

 gures, for which there has been no Method 

 (as far as I know) as yet made Publick. 



That the Reader may the more eafily 

 come at the Invention of thefe and the like 

 Theorems, I mall fubjoin another, and more 

 hereafter, if need be. 



Let therefore (%. 40.) ACF be a Se- 

 micircle, ADE a Geometrically Irrational 

 Curve, whofe Ordinate BD cuts the Semi- 

 circle in C. Let the Quantities be denoted 

 as before, viz. the Diameter AF — 2^, the 

 Abfciffe AB —y, the Are AG as v^ the Or- 

 dinate BD— £y and let & = rv*y\ an E- 

 quation exprefling the Nature of the Curves 

 ADE, in which r denotes any given and de- 

 termin'd Quantity, and n an indefinite Ex- 

 ponent of the indetermin'd Quantity I 

 fay the Area 



I ABD 



