a g4- Mifcellanea Curiofa. 



fer but by the Fluxion of either. There- 

 fore alfo o * : fF fF : F R. Qj E : D. 



PROP. VI. PROBLEM. 



(Fig. J 7.) To find the Curve KV by the 

 Evolution of which the Catenaria is <k- 

 fcriPd. 



Let (as before) AB=x, BF—j. Then by 

 . 



ax . 

 Tr&pojition II. y = , or 2axy z 4- 



V 2ax-\-xx 



ar*y* 3= 4* a: 2 . Wherefore (by the Newtonian 



Method which now generally obtains) 2axy z 

 • . • • ... . 



-\- ^axyy \ 2 x xy % -|- 2 (— 2^ata-, which 



becaufe of x = 0, fince the tonftant a; has 



no Fluxion, is) == 0. Therefore y = 



• . . • ■ • 

 i — . axy xxy a-\-x ax 2, 

 ( _-=) . X , 



zaxA-xx 2ax-\-xx 



putting inftead of y its Value 



V f iax-\~xx 



ax 



\Jiax-\- 



XX 



(For the Sign ~- before the Quantity de- 

 notes 



