CALCVLl VAKIATIONVM. 83 



C a fu s III. 



55. Si fuerit 

 4Z=:.LdU-\-VdW-{-mdX'{'Ndy-hVdp'^Qdq 



-{-Kdr -\- etc. 

 exiftente U—f^dx et U^^f^^dx, tiim vero : 

 ^'^-'^dx-^-fildj-^^dp+O.dq+Tiidr-i- etc. 

 *^'3'-^'dx-hdl'dj'-\-^'dp-\-£l'dq-\-di'dr+ etc 

 ponntur jLdxzzWj et JL'dxrzzW'jiic fado a:::^^, 

 fiat 



W — A et W^rrA^ 

 quo fadlo erir : 



m = ^-h-{A-W)^-h(A'-W'W 

 (P)=P-4~(A-W)q5-f-(A^-W^)^' 



(Q_)-QH-(A-W)O-i-(A^-W0.O/ 

 (Rj = R4-(A-W)Dl-|-(A^-W03i' 



etc. \ 



Cafus IV. 



57. Si 2 contineat formulam integralem UzJ^^dXj 

 \t fit: 



r/2-L^n-t-M^.v-hNt/jFH-P^/) -1- Q_^^4 R</r + etc. 

 quantiras ^ vero fbrmulam integraiem itzj ^dx^xt fit : 

 ^3 = S^7r4§9?«'^" + 9v^J>' + q5'/p + D^^4 3l^r+etc. 

 at J nullum porro integr.ile inuoluat , ita \t fit : 

 i/^-mdx-hndj-\-pdp-h<\dq-]-Vdr-i- etc. 



Ponatur J Ldx — W ^ et pofito xzza^ fiat W~A^; 



L 2. tum 



