CALCVLl VAKIATIONVM. 6^ 



Tariationum ipfius 2^.v , feu erit $JZdx::z/o Zdx. 

 Qjiod etiam hoc modo diftinAius oftendi poteft ; fit 

 JZcix:=:V, ita vt definiri oporteat oV; cum igituu 

 fit dWz^Zdx, erit $ dV — SZdxzzdSV ; Tnde fum- 

 tis integralibus fiet $W zzJ$Zdx. 



Problema ^. 



35. Propofita farmula integrali y 2 //a' . in qua 

 2 quantitas quomodocunque ex ipfis .v et j', carumquc 

 diiRrentialibus cuiuscunqne ordinis conflata , inuettigarc 

 cius variationem SJZdx. 



Solutio. 



Cum ergo Z fit fundio iplarum x,j,pyi],i\s ttc. 

 eias differentiale more confaeto fumtum huiusmodi 

 forraam habebit : 



dZ = M dx '{-Ndj + Vdp-i- QJq + R dr -^-Sds etc. 

 vnde eiusdem quantitatis 2 vnriatio erit : 



Cum mmc fit S jZdx:=:J SZdx , erit : 



<J ■}Z^xz:zjN$ydx+JVdh-rl^-\'J^fi'+ etc. 

 ne iam in vltcriori redudione exprcfiio § y turbet , 

 ponamus tautisper (5~ / — w , et redu(ftiones ita fe ha- 

 bebunt : 



J?d(ji — PiM-J(^d? 



f Q-d du _ Q db i fd_Q^j Qd« MdQ . ( udd Q , 



7 dx dx ~Jdx"^ — rfx — dx -^ J Tx~ 



/ R d^ [Q Rd^d co d R du) coddR / oj d^ R 



d*' — ii*» " dl^ ~r- d*» ""7 d«»~ 



£tC. 



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