Mifcellanea Cur i of a. 1 51 



Of the Quadratures of Geometric 

 cally irrational Figures. 



By J. Craig. 



LET ACF (Fig. 38.; be a Semicircle, 

 whofe Diameter is AF, ADE a Geo- 

 metrically irrational Curve, whofe Ordinate 

 BD cuts the Semicircle in C. The Quanti- 

 ties may be noted thus } The Diameter AF 

 =?= 2*, the AbfcifTe AB == j, the Arc AG — 

 % the Ordinate BD == z. ■: And let z. ~ rvy n 

 a General Equation exprefling the Nature of 

 the Geometrically irrational Curves ADE, in 

 which r denotes any given and determin'd 

 Quantity, and n an indefinite Exponent of 

 the indetermin'd Quantity y. I fay the Area, 



ABD = qv + V: 



lay —yy x 



ra 



— -f-Y rr / ~' + 



w-|-il 12 »x#-|-ii 2 

 aA%Zfr — 1 aB%2n* — .3 



^ ^ 2 -t- -/-M 



» 2 



*CX2ff — 5 ajytiin*- 7 



^-4 + __/-5 



3 ?/— 4 



