1 56 jMifceflanea Curio fa. 



Suppofing the Cube of the Arch of a Cir- 

 cle (correfponding to the verfed Sine) to be 

 the Ordinate of a Curve, vvhofe Abfcifle is 

 the fame verfed Sine j let it be requir'd to 

 find the Area of this Curve. 



Let the AbfcifTe be x 7 the Circular Arch 



v \ then the Fluxion of the Area is v 3 x. Let 



the Area be v*x — 7. Therefore v 3 x~\-$v z 



vx>—>q-=zv 3 x 7 whence q — ^v^vx. But v = 



dx • . $dv 2 xx 



therefore q ~ - — — -. But 



2 V ' dx- — xx 2*\/ dx—xx 



xx dx 

 (by The or. 2.) — *» == -■■■»■■ . 



V dx~xx 2 \j dx — xx 



y — v — y , and confequently q = idv*v-—* J- 



therefore q-=z%d<&* — s:dv 2 y. There- 

 fore now we are come to this, that the 



Fluent, of the Expreffion \dv z y 7 is to be 

 found. 



Let this Fluent be idv 2 y — -r. 



Therefore %dv z y-\- 3 dvvy> — >r — J dv 2 y. 



And confequently r—$dvvy—\ddvx* 

 Let r—-iddvx—*s. 



Therefore \ddvx—iddvx-\-iddxv>—<s. 



And 



