) 53 ( S-?S<« 



priorem formam reduci fe patiuntur : iam qnoque haud 

 praeter rem erit, vt iilas examinemus formulas diffcren- 

 tiales, quarum intcgiatio a pofteriori ifta formula depen» 

 det. In quo qiiidem negcnio aequum ert , vt a cafibus 

 fimpIicifTimis ordiamur, quo mclius patefcat, quo tenore 

 haec disquifitio procedat. 



§. 2. Supponamus igitur propofitas efle has binas 

 aequationes differentiales: 



I. x''ddj-{-a.xdj-\'(^xdz+ yy -{-B z — o j 



II. x' d d z + a'.v dy-\-g>'xdz-\- y' y-\- 5' 2; — o , 



in quibus difFerenridlium dx nulla ert habita confideratio, 

 quippe quum conflantia fint et vnitati aequalia fupponi 

 poirmr. Sumtis igitur differentialibus primis aequationum 

 propofitarum , habebimus: 



III. X' d'y -\- (2 + d) X ddy-V-^x d d z-\- {a-\-y) dy 



-f ((3 + 5) ^ 2: — o . 



IV.x' d'z-\-iz-\-§')xddz-\-a'xddy-{- {^'-\-y') dz 

 + («' -\-y') dy z^ o, 



tumque denuo his aequationibus iterum diiferentiatis 



V. x' d'y + {^-\-a)xd'y-\-{2.-\-za-\-y)ddy-\-^ x d' z 



-\-{2 ^-\-$)ddz = o, 



VI. X' d' z -\- {^-\- ^') X d'' z -\-{z -\- 2 ^'-\-^') d dz-\-a.' X d^ 



-\-{2a' -^-y^^ddy ~o. 



Vt nunc habeatur aequatio fola differentialia ipfius dy in- 

 voluens, fequens fiat combinatio: 



V. X' -4- in. X T -H IV.X' X -{- T. |x -h II. (J^' — o 

 tumque in aequatione refultanre coefficientes differentia- 



G 3 lium 



