||6 JMifcellanea Curiofa. 



Let AB (Fig. 3J be the Curve of the. Pa- 

 rabola," whofe Axis is AF, Parameter a ; let 



AEs=sat, EB^j, ABe=**, BDs*, DC^j, 



BC ;=:*.. The Equation exprefTing the Na- 

 ture of the Parabola, being axzzyy, we have 



ax t=s iyy 9 whence xmiyy\ but BC? s=: BD1 



4y*yy • • 



' b CD?, that is « sa xx ~\-yy + es 



4y*Xy and therefore z t=zyy qy* -V aa 



aa a 



my \/y* +* \ aa. If now by this Expref- 



2 a 



Son y V>* + % aa be thrown into an infinite 



Series, the Curve AB will eafily be known. 

 It appears farther, that giving an Hyperboli- 

 cal Space , this Curve is alio given, and vice 



verfa. For | ^ V> 2 + i and confe- 

 quently i az, is the Space whofe Fluxion is 



y *sjy % H(t I But fuch a Space is no other 

 than the Exteriour (Equilateral) Hyperbola 

 A BEG, whofe Semiaxis AB j=*i'i% its Ab- 

 fcifle AE ^j, and its Ordinate EGzzx. 



For 



