CALCVLl VAKIATIONVM. 69 



vtcnnque compledatur , in qua autem fit ^ fundio 

 ipfarum x, j, p, ^, r, s etc. definire variationera for- 

 mulae illius integralis J7.dx. 



Solutio. 



Cum quantitas Z praeter quantitates x, y, p, q^ 

 r, s etc. etiam formulam integralem Tl—f^dx in- 

 voluat , fpedari poterit tanquam fundio qaantitatum 

 n, X, j, p, ^, r, s etc. vnde fi more folito difFeren' 

 tietur , prodibit talis forma : 



dZ — Ldn^m dx + N ^/ 4-P^/>+Qf/^+R^r+-S</i ctc. 

 vnde colligitur variatio ipfius Z : 

 ^Z — L<5^n + N^jr+P5-p + Q.^^ + R^r + S<5'i + etc. 



Cum deinde fit 3 fundio ipfarum Xj y, p, q. r, s etc. 

 ponatnr : 



d^-^dx-h^dj-^-^^dp-i-Cidq-^-dtdr-hiQds-^-etc. 

 atque ex praecedente problemate erit ^n, feu 



•4- "dT-vQ—dT 4- "d^ " etc.) 

 H-"?Cm-^-f-t-etc.) 

 + n.'(®-ctc.) 

 Vel fumatur potius prior forma : 



$Jsdx-jr,$jdx^-^/^d$j-{^f^^^'-^f^y 



I 3 eritque 



