125 de methodo 



J2.dx valorem omnium maximum vel minimum adi- 

 pifcatur, eas ita definiri conuenit , vt tam pofitOA;z:o, 

 quam x^a, etiam his aequationibus fatisfiat: 



/T-.\ d(Q.) , d d(R) ^ /r\\ d (R) ,rt\ 



(P)- ir + Wetc. ro- (Q)--^W.ro-(R)-etc.=:o. 



Coroll. 5. 



Si fundlio Z non fojum duas huiusmodi formulas 

 integrales ^r^if^dx ^ ^'^^'^'dx ^ fed etiam plures 

 ^)//— /3^^</a; , (^^^^ rzf^^^Ux etc. inuoluat , ita ta- 

 men , vt litterae ^i 3 ' 3^^ ^^^' ^^ootent tantum fun- 

 diones quantitatum x^ j, p, g, r etc. neque vltra vl- 

 las formulas integrales inuoluant ; ex folutione proble- 

 matis etiam huiusmodi fbrmularum variationes difFeren- 

 tiales facile aflignantur. 



ProbJema 4. 



Si fundio Z praeter quantitates Af,j',/», ^, r etc. 

 etlam formulam integralem ^z::::.J^dx vtcunque im- 

 plicet , vt fit 

 dZ—hd^-^-Udx-^-l^dy-^-Vdp-^Qdq-^Kdrttc, 



fundio autem 3 ^^^^^ praeter .v, y, p, q, r, etc. aliam 

 denuo foimulam integralem (p=zj^dx inuoluat , 

 vt fit 



d^~£d(p + ^dx-]-^dy-\-^dp'\-0.dq-\-f!ltdr + etc. 

 fundio vero t tantum ex quantitatibus x,j,p,q,rQtc. 

 fit compofita , exiftente 



dl-mdx-^-ndj^pdp-^-^idq-^Vdrttc. 

 definire relationem inter x et j , vt haec formula in- 

 tegraliij /Z^A* , quatenus a termino x — o vsque ad 



termi- 



