Quare pofita 2 — 0, fiet eiusmodi exprefllo integrata 



Eft autem radiiis ofculi in genere 



(dx' -H dy') y (^ jr' -h dy') -. — dxddy. 

 Ergo Aequationcm Catenariae difFerentiando, pofita dx 

 conftanti, erit 



ddy~{—a''—ax)dx*;{2.ax-\-x')V{'i.ax->t~x^)^ 

 idcoque radius ofculi ^f-it-^ . Facta itaque .v — o , erit 



ofculi radius R' in vertice A — a. Ergo impulfus tan* 

 gentiales in Catenaria aequabuntur a' -h x. Q_. E. I. 



CoroIIarium» 



§. 23. Hinc impulfiones Fornicum ex Circulo, 

 atque Catenaria, communi vertice A et amplitudine extruc- 

 torum, eadcm poflta ponderum fuperincumbentium lege, 

 inter fe comparari poterunr. Definiatur itaque in primis 

 circuli radius, qui per pundla Catenariae tranfeat A, D, C. 

 Verrice A , et pararaetro S A B — 8 <? defcribatur Para^ 

 bola Conica AL, et producatur ordinata CD, vt Para- 

 bolae occurrat in L. Ea efl Catenariae proprietas, vt 

 dimidius Arcus Parabolae AL aequetur femiordinarae KD. 

 Quare arcus A L — K D in jr et conflantes deiiniendus 

 eft , qui, methodo redificationum tritifTima, inuenietur 

 huius formae; 



a Bf , ^ _ 7 / g^O \ 



(V(j a*-*-4a-;- V(2 a j:))* ' \V (»« *-*-♦<>") — V (a a jc)a 



(V f2 g jc -H 4 o») — V (2 a a:))» 



Ponatur is — P, erit KDzr?. Sit infuper fagitta For- 

 nici& Pi.K—by P' id^ in quod vertitur |, lubftituto If 





