1 3 o JMlJcellanea Cur to f % . 



gives x n x for the Fluxion of the Are?, 



n 



and confequently the Area fought is 



m \ 



x n , or (fubftituting y inftead of 

 n 



" — x y* 



m-\-n 



Again, fuppofe a Curve, whofe Equation 

 is x^-Yaaxx^yy (which is the firft of the 

 Excellent Mr. Craig's Examples) putting y s=s 



x V ' xx"\- aa, the Fluxion of the Area will be 



xx\/xx -\~ aa. Which Exprefllon involving 



a furd Quantity i let us fuppofe \jxx\~ aa^zz, 



then will xx-Y aa ^ z, 2 , and confequently 

 • ■ • • 



[xkiZzjL^ and fubftituting tz, and z. for xx 



and \l xx~Y aa, the Fluxion thus freed from 

 Surds, will bex,~z: ; which reduced to its Ori- 

 ginal | z} and putting V ' xx-Yaa for we have 



Yxx-Yaa ^1 xx -~Y aa for the Area fought 



But to fliew more efFe&ually how eafily 

 thefe Quadratures are perform'd, 1 fhall add 

 one Example more. Let the Equation of the 



x z x 

 Curve be ■ & jr, therefore y g , 



x~Va j—~ 



» , * • » - }' _ ' 



and : therefore ; is the Fluxion of the 



%/k\-m Area* 



