iio Miscellanea Cur to fa. 



And confeguently if Dd expounds the ab- 

 solute Gravity of the Particle Dd (as it will 

 be in a Catena equally thick) then d^ will re- 

 prefent that part of the Gravity which ads 

 perpendicularly upon Dd, and by which it 

 comes to pafs that dD (being by the flexibi- 

 lity of the Chain moveable about d ) endeavours 

 to bring it felf into a Vertical Pofition. And 

 therefore if M (or the Fluxion of the Ordi- 

 nate BD) be Ccnftant, the A&ion of the Gra- 

 vity exerted perpendicularly upon the cor- 

 refpondent parts of the Catena Dd, will alfb 

 be ccnflant, or every where the fame. Let 

 this Action or Force be expounded by a. 



Farther , From the above cited Proportion 

 in Mechafticks, DcT or the Fluxion of the 

 Axis AB, will expound the Force to be ex- 

 erted in the direction dD, which is equiva- 

 lent to the former Endeavour of Dd (by which 

 it tends to bring it felf into a Vertical Pofiti- 

 on) and is fufficient to hinder it. 



But this force arifes from the Line a Gra- 

 vis DA pulling with the direction dD, and 

 is confequently (all the reft continuing as be- 

 fore) proportional to that Line DA. There- 

 fore /d, the Fluxion of the Ordinate, is to 

 J*D, the Fluxion of the Abicifle, as the con- 

 ftant right Line to the Curve DA. Q,: 

 E : F. - , ; 



C O R O L. 



If the right Line DT touches the Catena- 

 rian and meets the Axis AB p.roduc'd in T, 

 then will DB : BT : : (d^ : cfD : :) a : DA 

 Curve. 



PROP. 



