JMifcellanea Curiofa. 2 3 1 



And confequently (fince they arife together) 

 the faid Superficies of the upright Cylinder 

 is equal to the Hyperbolical Space ALH. 

 Which therefore divided by the Pondus it 

 felf AF, or its equal the right Line AL, gives 

 the right Line AE, for the diftance of the 

 Center of Gravity from the Axis of Libra- 

 tion GL. So that the point E is the Cen- 

 ter of Gravity of the Curve FAD, lying e- 

 qually on both fides the Axis. Q,: E: D* 



COROL. I. 



The Spaces ABHL, BAH, and AFG, are 

 in Arithmetick Proportion. For the Fluxion 



• • 



ax~\-xx 



of the Space ALH is (= x x = 



%Izax~\~x* 



ax-\-x 2 x x 2ax~\~x* — ax x x 



*\Jiax-[-x 2 Sfiax—x % 



, — axx 



x V 2ax-[-xx—* — ) = to the Fluxion 



of the Space BAH lefs the Fluxion of the 

 Space AGF, by Propofition IV. And fince 

 thefe three Figures do arife together, it fol- 

 lows that BAH — AGF = (ALH BL — 

 BAH. Wherefore 2BAH = BL + AGF. 



Q, 4 Whence 



