ill JMijcellanea Curiofa. 



AP ( = P P = VVi-Pn* ) = y/*££ 



2ax-\~xx 



•=.^1 2ax z Ar*x 2 7 which is equal to 



x *\I iax~\-xx 



as appears by multiplying both Numerator 



and Denominator into \l 2a~\-x. And fince 

 HF is every where ■= AP, the Fluxion of 



2ax-\-xx 



HF that is mh-\-sfc fliall == . But 



\j xmx^xx 



ax A- xx 



we have hitherto found mh 



\/ 2,ax\-xx 



Therefore sf (the Fluxion of BF the Ordi- 



. * ax 

 nate in the Catenaria) = — — , — — . • and 



\/ 2ax-\-xx , 

 confequently the Fluxion of the Curve AF 



(that is, Ff = \fsfi-\-Fs! = V ^ J~ & \ 



2ax-\-xx ' / 



• • 



ax-\-xx 



is = — — the Flowing Quantity of 



*\J 2ax-\-xx 



which 



