1 3 2 ikf ijcellanea Curio fa . 



of the Sph ere, and con fequently the Portion 



it felf is 4 5 d?Ar a -h j* 3 , and the circumfcrib'd 



Cylinder is 4 <^v* -<,v 3 . Therefore the Por- 



tion of the Sphere is to the circumfcrib'd Cy- 

 linder, is as i d f a.- to d >—* x. 



The Rettification of Curve Lines will be ob- 

 tain'd, if we confider the Fluxion of the 

 Curve as a Hypothenufe of a Re&angular 

 Triangle, whofe lides are the Fluxions of 

 the Ordinate and Abfcifle. But in the Ex- 

 preflion of this Hypothenufe, care muft be 

 taken that only one of the Fluxions be re- 

 maining, as alfo only one of the indetermi- 

 nate Quantities, viz. that whofe Fluxion is 

 retain'd. Some Examples will render this 

 clear. 



(Fig. 1.) The right Sine CB being given, 

 to find the Arch AC Let ABzsx. CB^y. 

 OAnr. CE the Fluxion of the Abfcifle, 

 ED the Fluxion of the Ordinate, CD the 

 Fluxion of the Arch CA. From the Pro- 

 perty of the Circle irx xx ~yy, whence 



irx*-* ixxzz iyy 7 and therefore yy. But 



r x 



C D? s yy -\- xx j=! yy ^y 2 yy r=\yy + 



rr >— irx 4" xx , 



• '. ry 



y*yy r ?yy ; therefore CD s=! -2 



