Mifcellanea Curio fa. 225 



tma) of approaching direftly to the Axis,' is 

 to the force of defcending perpendicularly 

 in the fame (or that part of the fuflaining 

 force that ads in the dire&ion BD, is to that 

 part that ads in the direction DcT) as the 

 Semiaxis of the Conterminal Hyperbola AH, 

 to DA the length of the Catena to the Ver- 

 tex. Whence, the Catena being ^iven, this 

 Ratio is alfo given. And in the fame Ca- 

 tena^ iufpended with different degrees of 

 Laxity, that Horizontal force, is as the Axis 

 of the Conterminal Hyperbola \ fince DA 

 remains the fame, if the Extremities be 

 equally high. 



COROL VI. 



The Catena placed in an Inverted Pofition 

 in a Vertical Plane, maintains its Figure and 

 does not fall down \ and fo makes a fine 

 Arch or Fornix. That is, very fmall hard 

 flippery Spheres, difpos'd in the Inverted 

 Catenaria, will form an Arch, no part of 

 which will be thruft inwards or outwards by 

 the reft, but (the loweft Points continuing un- 

 mov'd) it is preferv'd by vertue of its Fi- 

 gure. For fince the Pofition of the Points 

 of the Catenaria^ and the Inclination of the 

 parts to the Horizon, is the fame, whether 

 it be in the Pofition FAD, or in an Invert- 

 ed Pofition, provided the Curve be in a Plane 

 that is perpendicular to the Horizon, it is 

 evident that it preferves its Figure unchang- 

 ed, equally in one Pofition as the other. 

 And on the other hand, the Catenaria are 

 Q. the 



