MOTVS FLVIDORVM. 279 



18 Erit enim vti ex elementis conftat : 

 VprR — ^KiFp-^Rr) 

 RrqQzzz JRQ(Rr-l-Qf) 



Pp?Q:=:SPQ(Pp-r-Qfl 

 His igitur colligendis reperietur : 



Apqr~ iPQ. Rr-iRQ. Pp-£PR. Q<f 

 Ponatur breuitatis gratia 



AQ=AP-fQ; ARrrAP+R; Qqzzi?p+q et Rrz?p+r 

 Yt fit PQ^Qj PR = R et RQ=Q-R, 



eritque A*tfr=iQ(Pp-Hr)-tfQ-R)Fp-SK(PpHr-f) 

 fme Apqrzzr.ZQ.r-^R.q. 



19. Eft vero ex valoribu9 coordinatarum ante 

 exhibiris 



Qzzzdx-\-Ldxdt : qzzzMdxdt 

 Rzzz /dydt; rzzzdy-\-mdy dt\ 



q«ibus valoribus fubftitutis, orietur area trianguli 



pqrzz\dxdy(i+Ldt)(i-\-mdt) ~\M/dxdydt\ fiue 

 pqr~ldxdy{t-\-Ldt +-mdt-\-Lmdt z -M/dr) 

 quae cum aequalis erte debeat areae trianguh /mn , 

 quae eft zzldxdv , haec nafcetur aequatio: 



Ldt -±-mdt-\- Lm dt* - M Idt* zzz o fiue 

 L -\-m -h-Lwdt -M/dt zzzo. 

 20. Cum igitur termini Lmdt et MA// prae 

 ^nitis L et m euanefcant , habebitur haec aequatio 

 L-\-mzzzo. Qnm ob rem, vt motus fit poffibilis, ce- 

 leritates u et v pnn<5ti cuiuscunque /, ita debent efle 

 comparatae , vt pofitis earum differentialibus 

 duzzzLdx-\-/dy } et dvzzzMdx-\-mdy 



fit 



