2 3 2 -Mi/" 'sellanea Curio f % . 



Whence 'tis plain that the Spaces BL, BAH, 

 and AGF, are in Arithmetical Proportion, 



COROL II. 



The Center of Gravity of the Catenaria, 

 is the Lowefi of all thofe Lines that have 

 the fame Termini, and are of the fame 

 length. For a heavy Body will defcend as 

 far as it can. And fince the Figure it felf 

 defcends as much as its Center of Gravity 

 defcends *, 'tis manifeft that a flexible heavy 

 Line, will difpofe it felf in fuch a manner, 

 as that its Center of Gravity may be low- 

 er, than if it aflum'd any other Figure. 

 And from this one Property of fuch a Line, 

 all the reft may eafily be deduced. 



COROL. III. 



If there be upright Cylinders ereded upon 

 any fort of Curves, that are of the fame 

 length, and have the fame Termini D and F, 

 with the Catenaria FAD ; and thefe Cylind- 

 ers be cut by a Plane pafling through DF \ 

 then the greateft of all thefe Superficies (hall 

 be that which Hands upon the Catenaria. 

 For thefe Superficies (if the Angle contain'd 

 under the Planes be half a right one) divi- 

 ded by the Curves (which in the prefent 

 Cafe are all of the fame length) give the di- 

 ftances of the Centers of Gravity from the 

 right Line DF. And fince this diftance is 

 greateft in the Catenaria (becaufe of the 

 greateft Defcent of the Center of Gravity > 



therefore 



