130 DE METnO DO 



Coroll. 3. 



Ex his iam facile coUigere licet , fi etiam fun- 

 Aio t nouam fbrmiilam intcgralem inuoluat , quemad- 

 modiim tum variatio difFerentialis exprimatur ; fi fcili« 

 cet fuerit </j^ — (.'/(J)^-4-ltt^.v-f-etc, tum ad ff^rmulas 

 V=fLdx et ^=r/£V^A' infupcr tertia X>-f\^dx 

 accederet j reliqua attendenti facile fe ofFerent. 



Problema 5. 



Si fundlio Z , praeter quantitates x^ y, p, q, r etc. 

 ctiam formulam integralem ^—f^dx vtcunque im- 

 plicet , vt fit 



dZz:^hdO-\-Udx-\-]<!^dj~>rVdp-\-QJq-\-Kdrtiz. 

 fundio vero 3 praetcr quantitates at, j, p, q, r etc. 

 eandem denuo formulam integralem O—f^dx inuol- 

 vat , vt fit 



d^-^dO-^-^Sridx-^-^dj-^-^dp-hCldq^^drac. 

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

 tegralis /Z^A' , quatenus a termino .v:=ro ad termi- 

 num datum x^a extenditur, maximum minimum ve 

 valorem adipifcatur. 



S o 1 u 1 1 o. 



Variatio differentialis eft, vt hadenus , 



BfZdx—fLdx$^-\-j:^dxSy+f?dx$p-\-fqdx$q 



-\-f R dx ^ r etc. 

 deinde vero habemus $ ^ — $ f^dz—f^^^dx et 

 ^d> — t^^-\-Tv^y'\-^$p-\-0.oq-\-tii^rctc. 



Cum 



