Mifcellanea Curtofa, 24.5 



determin'd by this Conftru&ion, are equally 

 diftant from the point C. But they are alfb 

 pofited in the fame right Line, and towards 

 the fame parts, and therefore they coincide 

 with one another. This Coincidence of the 

 point E as determin'd above, with the Cen- 

 ter of Gravity as found at Prop, V. may be 

 thus fymhetically fhewn. By Cor. I. Prof. V. 

 2BAX = AYD-I- BAx AR. Whence AH + 

 2BAX = (ACHD + BAx AR = by Cor. fore- 

 going) ARx CA BAx AR ; that is, BDx 

 AC -f 2BAX =ARx CB ; or BDx AC ~ AR 

 xCB — 2BAX. Whence BDxAC-|-ADx 

 BC — (ADxBC-f ARxCB — 2BAX — 2AD 

 xBC- — 2BAX ==) 2ADx AC-|- 2ADXAB — 

 2BAX. And dividing by 2 AD, we have f 



BDx AC , > un __, An 1 ABxAD— BAX x 

 + i BC - (AC+ 5i5 -) 



CA^t— But— is the diftance of 

 AR AR 



the Center of Gravity of the Catena from the 

 Vertex A, determin'd at Prop. V. and confe- 

 quently, according to the 5th Proportion CA 

 ARX 



-U - [s the diftance of the point E from 

 AR 



, BDx AC . , ' . , ,. n 

 C - 0 now 2 " Aft" + i B Q 1S * ne diftance 



of the point E alfo from the fame point C ac- 

 cording to this Cor. Whence 'tis manifeft that 

 thefe two Determinations of the point E 



ARX 



amount to the fame ; becaufe CA + -vrr* 



AR 



t BDx AC . 



i — + 5 BC. 



R 3 C O R O L. 



