So CFRVATFRA LAMINAE 



'\-adsdx(}y -f- aydsddx^zz C dsddx , v n d e --_g-_ rrz 

 ^^'' —^J^-l^-^-- qiiae iiueii^ita ubit 



adi dx ads • dx-^ads i o 



in hanc •=!_'-/( t-</j--/7r^,0=J-/^°A^ -f- -\Ibds. Ereo 

 c-^y-_djc^adi {Qucdx-ajdx—bdx-^ahds.Sit c-h-e-y 

 crit r/:i'^ {e—ay)'^ — aahhds- confcquenter dx — 

 -% vt AP fit axis, of ortet fit r/;':^.r— 0;i. fi 



V [e—ay) -aabb) 



j~o erit ergo e—-\-ab. ideoque dx— — ^^^ 

 V^iuie elt aequatio pro catenaria eademque manet 

 quomodocunque a varietur, vt ergo non a ponde- 

 re fili pendeat. Hoc autcm it.^-accidere oporte- 

 re ex eo patet , quod tam vis venti, quam graui-r 

 tatis leorfim eandem catenariam producant. 



Sit vis normalis quoque conftans,nempe r/N= 

 bds erit brds-^ardx--\-ayds—cds. quia veror— ^^ 

 erit bdsdy-\-adxdy-{-ayddx—cddx , quae integraciac 

 ^~—bds-\-adx. Sit ezz:hc-\-ac \ tni cds—cdx—byds 

 -aydx. atque dx — - — ^'=±^y.^-.. 



Vrohkma. Si curuae AMB in quouis pundo 



Fir iJ- ]\| duae potentiae applicatae fiierint,quarum altera 



normaiis in curuam vt MN,altera tangentialis MT; 



inuenire aequationem pro curua , quam format fi- 



lum perfede flexile. 



Solutio. Refoluantur ambae potentiaein late- 

 rales , quarum vna verticalis altera horizontalis, 

 ncmpe MN in MR et RN, et MT in MS etTS-,Erit 

 f/P— MR-+-MS et ^QpNR-TS. Sit autem MN=:= 

 ^N. et MT~^T. Erit MR— ^,NR— ^^-, MS=: 

 «^etTSz:^^. Ergo ^^ iz^ i^il^ et 



dQ^ 



