Mifcelhinea Curiofa. 



PROP. II. THEOREM. 



(Fig. 1 4.) If upon tk e Perpendicular AB. 

 as an Axis, and the Vertex A, an E- 

 quilateral Hyperbola AH be defer iVd, 

 'Uofe Semi axis AC ^3 a; as alja upon 

 the fame Axis and Vertex, a Parabola, 

 AP tvhofe Parameter is quadruple the 

 Axis of the Hyperbola, and the Ordi- 

 nate of the Hyperbola HB be always 

 produced till HF be equal to the Curve 

 AP : / fo) then, that (making BD and 

 BF, equal) the Curve V AD, in which 

 the Points V, D, are pofited, is the Ca~ 

 tenaria. 



Put AB t= x 1 then Bb =-#, and BH == 



\f 2 ay-\~xx' 0 whence (from the Method of 

 Fluxions) the Fluxion of BH, that as 



^ 1- XX 



_J w . Again, fince the Parabola AP 



V iaxA-<xx 



has for its Parameter 8*, BP ftall = SSax, 

 Whence the Fluxion of BP, that is 4 = 



"tlL. Wherefore the Fluxion of the Curve 



AP 



