Mifcellanea Curt of a. 247 



librated Figure PFADH (~ 2 CAxAD 5 by 

 Cor. V. of this Prof option) there will arife 

 (for the diftance of the Center of Gravity of 

 the Figure PFADH from the Axis PH) % 



+ % CB h which is = i CE deter- 



min'd above. 



COROL VIII. 



If through the point N where DT the 

 Tangent to the Catenaria in D, cuts the 

 Line AR, be drawn a Parallel to BC, meet- 

 ing in O a parallel to AR drawn through E ; 

 then will O be the Center of Gravity of 

 the Curve AD. For by Cor. 6. the Center 

 of Gravity of the Curve AD is in the right 

 Line EO. But it fhall be demonftrated to 

 be in the right Line NO ; and confequently 

 that O it felf fhall be the point. Let DA 

 be conceiv'd to be librated upon the Axis 

 HL ; then the Momentum of this is the 

 Curve DA multiplied into the diftance of 

 the Center of Gravity from HL. And 

 confequently its Fluxion — DA x Hh (Hh 

 being the Fluxion of the diftance of the 

 Axis of Libration from the Center of Gra- 



V » ■ ax 

 2ax-\-xx x — — — = ax. And 



\/iax-)~x 2 



therefore the Momentum of the Curve DA, 

 with refped to the Axis HL, is = ax. And 

 confequently the diftance of the Center of 

 Gravity from the fame Axis, is ax divided 

 R 4 % 



