CALCVtl VAKlATIOnVM. 85 



Cafus VII. 



60. Si 2 contineat formulam Tlzzj^d x,yt(\t: 

 /fZ-L^n4-M^.v-hN^>'H-Pr//) + Qfl'^+R^r+etc. 

 tiim vero ^ deniio eandem formuhm Yl:z:J^dx iii- 

 voluat, vt fit : 



^3-g^/n-f-f5)Jr/.v + 9^^j + q5^p+D^^+9l^r+etc. 

 Vomim j^dx—^ , et pofito x — a, fiat SS3 = 5( ; 

 deinde ponatur J tf— ^-^^L^o; — W, et pofito A'— <?, fiat 

 W — A , ericque 



(N)=:N+-f^'^(A-W)f)(J 



(P)=:P+f3i-^(A-W)q> 



(R)-R-h^2i-2B(A-W)Dt 

 etc. 

 di. Simili modo hanc inueftigationcm ad alias 

 formulas complicatas extcndere licet , verum cum tales 

 vix vnquam occurrere fbleant , labor fuperfluus foret. 

 Cum igitur fbrmularum integralium tam fimpliciorum, 

 quam magis compofitarum, variationes definire docuerim, 

 calculus variationum fere penitus abfolutus videtur j quo- 

 modocunque enim quantitas varianda fucrit, tam ex for- 

 mulis abfblutis, quam inregralibus , conflata , ope difieren- 

 tiationis ordinariae eius variatio reperiri poterit. Veluti 

 fi quantitas varianda U contineat formulas integrales 

 quascunque : 



(p-f2dx; ^'=:fZ'dx; (^''=JZ''dx etc. 

 differentietur ea more folito , prodeatque : 



^ U — K ^$ -h K VO^ H- K^^^d)^^ ctc. 



L 3 tum 



