Mifcellanea Curiofa. 24.3 



COROL IV. 



Hence alfo it follows that if the Angle 

 BDT be equal to AGR, the right Line DT 

 touches the Catenaria in D. For then it will 

 be (in the fimilar Triangles DBT, CAR) 

 DB: BT : : CA : AR, or CA: Curve AD 

 which is = AR. And confequently DT 

 touches the Catenaria^ by Cor 0 1. Prop. I. 



COROL. V. 



tt follows alfo that the Space ACHD = 

 the Rectangle CAxAR. For becaufe (by 

 Prop. IV.) AYD—CAx (AD— BD, =AR~ 

 AY, by Cor. III. of this Prop. =) YR • the 

 thing is manifeft. And fince CA is given, 

 'tis plain that the Space ACHD is as the 

 Curve AD, and the Fluxion of the former 

 Hd, as the Fluxion of the Latter Dd. 



COROL. VI. 



If through the point K where CR cuts HD, 

 we draw KZ parallel to PH, meeting AC in 

 BC-I-CZ 



Z, and tike CE == — — — \ then will E be 



2 



the Center of Gravity Sf the Curve FAD. 

 Imagine an upright Cylindrick Superficies 

 ere&ed upon FAD, and to be cut by a 

 Plane 'paffing through PH, and making an 

 Angle of 45 with the Plane of the Curve 

 FAD. This Superficies, will expound the 

 R 2 Momen- 



