Mifcellanea Curiofa. i\j 



The Properties of the Gate- 

 naria. 



By David Gregory, M. 2). Savu 

 lian Trofejfor of Aflronomy ] > and 

 F. R. S. 



PROP. I. PROBLEM. 



To find the Relation of the Fluxion of 

 the Axis y to the Fluxion of the Qrdi- 

 dinate in the Catenaria. 



LET FAD be a Catena hanging on the 

 Extremites F and D, the loweft point 

 of which (or the Vertex of the Curve) is A, 

 the Axis AD perpendicular to the Horizon, 

 and the Ordinate BD parallel to the fame. 

 We are to find the Relation between Bb or 

 Dc^, and d/ ; fuppofing the point b infinitely- 

 near to B, and bd parallel to BD, as alfo 

 D<T to BA. 



From the Principles of Mechanicks, 'tis 

 plain that three Powers which are in Equili- 

 bria, are in proportion to one another, as 

 three right Lines parallel to their refpe&ive 

 Directions (or inclined in any given Angle 

 to them) and terminated at their mutual In- 

 terferon. 



And 



