Mtfcellanea Curio fa. 



by AD, or But becaufe DT 



AR 



touches the Catenaria, by Cor. 4. of this Pro- 

 fofitkn, the Angle BDT, or DNY—ACR, 

 and the Angles at A and Y are right ones, 

 therefore in the Equiangular Triangles 

 RAC, DYN, 'tis RA: AC:: DY : YNj 

 A f Y DY 



whence YN = - - that is YN is the 



RA 



diftance of the Center of Gravity of the 

 Catena AD from the Axis HL - 7 or that Cen- 

 ter is in the right Line NO. 



COROL IX. 



If through the point I be drawn a right 

 Line parallel to AR, meeting ON produced 

 in W , then W (hall be the Center of Gra- 

 vity of the Space ACHD. For by Cor. 7. 

 the Center of Gravity of the Space ACHD, 

 is in the right Line IW, but it fhall be de- 

 monftrated alfo that 'tis in MW, and confe- 

 quently W is the point. For (after the 

 fame manner as inCor. foregoing) the Fluxion 

 of the Momentum of the Space ACHD ponde- 

 rating upon the Axis HL, will be fhewn to be 



(ACHDx Hh= ACx ADx Hh=) a V iax-\-xx 

 ax 



x r= a*x. And confequently the 



V ' iax-\-xx 



Momentum of the Space ACHD, with re- 

 fpeft to the Axis HL, is the Fluent of this 

 ^ Fluxion, 



