CALCVtl VARIATIOnrM. «77 



Corollarium. 



47. Si ergo qiuntitas Tarianda O definiatur per 

 hanc aequationem difFerentialecn dO~2,dx, in qua Z 

 inuoluat vtcunque ipfam quantitatem O et infuper lit- 

 teras r, j, p, <j, r etc. eius variatio ^ O per hoc pro* 

 blema adignaci poterit, 



Problema 7. 



48^. Si in formula integraii Q>^j7.dx quaniitas 

 Z praeter litteras .v, y, p, q, r etc. non (blum ipfam 

 quaniitatcm <S> , (ed inlhper ndhuc aliam formulam in- 

 tegralcm Y\ zz f^ d x quomodocunque implicet , in 

 qua autem quanticas ^ tantum pcr litteras x ^ j , p ^ 

 q^ r etc. dctur ; inuelbgare variationem huius formulae 

 ^Q^izr^JZdx^jSZdx. 



S o r 11 1 i o. 



Cum Z fit fundio quantitatum x^ y, p, (^, rerc. 

 infuperque formularum O — /Z^o:, et fl rr y^^.v, prae- 

 beat ea diflferentiando : 



dZ — KdO -{-Ldn-^Mdx-hNdf-i-Vdp -{-Qdq-^- etc. 

 vnde eius variatio erit : 



^Zr:K<5cl>^-L^n-f-N5>-4-P^t'.-+-(^'^+ etc. 

 Porro autem cum ^ ^t^ fundio litterarum .v, j, p, q, 

 r etc tantum ponatur : 



<^3 - ^ dx H- ^ dy -t- ^dp -h 0^^ 4- 31 ^r + etc. 

 eritq' le ob 5^ n —j^ ^ ^^ 



^n-,Sdxi.my\^'!i^D'B\%'S^^,iz.) 



K 3 Ponatur 



