Mlfeellanea Curio fa. 24.9 



Fluxion, a*x, that is, a 2 x. This therefore 

 divided by the Space ACHD, or 



ax*\J iax-\-xx, gives the diftance of the 

 Center of Gravity (of the Space ACHD) 



ax 



from the Axis HL, which is 



V f 2ax-\-xx 



__ACx DY^ ^ therefore the Center of 

 AR 



Gravity of the Space ACHD, is in the Line 

 NW. And fiom thefe two laft Corollaries^ 

 is found the Center of Gravity of any Por- 

 tion of the Catena , though not reaching 

 the Vertex A, or alfo of any Space com- 

 prehended under any Portion of the Cate- 

 tiaria^ and any other right Lines befides 

 thofe aforefaid. 



COROL. X. 



Hence are meafur'd the Surfaces and So- 

 lids generated by the Rotation of the Ca- 

 tena (or a Space comprehended under it, 

 and a right Line) about any given Axis. 

 For a Figure generated by fuch a Rotation, 

 is (as is vulgarly known) equal to the gene- 

 nerating Figure multiplied into the Periphe- 

 ry defcrib'd by the Center of Gravity in the 

 Rotation, which Periphery is given, fince 

 the Radius or Diftance of the Center of 

 Gravity from the given Axis, is given. Thus 

 if the Catena AD roul'd about the Axis AB, 



then 



