0.2O Mifcellanea Curiofa. 



C 0 R O L. 



Hence it follows that the Space FADf 

 comprehended under the Catenarta and Hori- 

 zontal Line FD, is equal to the Re&angle 

 under FD and BA, lefs the Redangle un- 

 der either Axis of the Hyperbola AH, and 

 DH the excefs of the right Line BH or the 

 Curve AD, above the Ordinate BD. 



P R O £. V. THEOREM. 



(Fig. 36.) If to the right Line AL be ap- 

 plied the Rectangle LE, equal to the 

 Hyperbolical Space ALH, then E will 

 be the Center of Gravity of the Cate- 

 naria AFD. 



Let the Curve FA be conceiv'd to be li- 

 brated upon the Axis GL. Then (from the 

 Dodtrine of Centers of Gravity) it is mani- 

 feft that the Momentum of the ponderating 

 Cvrve FA is expounded by the Superficies 

 of an upright Cylinder erefted upon FA, 

 and cut off by a Plane, pafling through GL, 

 and making an Angle of 45 0 with the Plane 

 of the Curve. And the Fluxion of this Su- 

 perficies or FA x FG, is equal to the Fluxion 

 of the Space ALH or BH x HL ; becaufe 



FA, BH 3 as alfo FG and HL, are equal. 



And 



