i82 DE CRITERIIS INTEGRABIL. 



i; X; fJt; V etc. ope qiianiitatum I, L, M, N etc. 

 dcterminentur. 



39. Relationes igirur has inueftigaturi , ne iti 

 nimis prolixos incidamus cakulos , ftatuamus mox 

 fequentes ip(iirum i , X , [a. etc. valores 



izzfjn^xdytiz + a-, -Kzzf)fhdxdydz-+^ ; 



Y.—fff^\dxdydZ'\-y\ y—fff^dxdydz-^-B ; 



ii^/ffVdxdydz-hi', ii^zz/f/V^dxdydz-hs'; 



7i*'-fffY"dxdydz-^t" ; Kz:zfffqjxdydz-\-^; 



Wzz-ff/^^dxdydz-^-^^ etc. ctc. 



Deinde quum fit 2zz//fW dxdvdz ^ patet quoque 

 cffe d\ zz { ^l\^ ' Si proinde \alor fuppofitus 

 ipfius dY comparetur cum eo, qui ex difFerentiatione 

 formulae ^Z oritur , faciUimum erit \alores littera- 

 rum a, (3, y detcrminare, \nde deinde i, A, ^ji, v etc, 

 dettrminabuutur. 



40. Habemus vero primo, fumendo difFerentiale 

 ipfius dTL pofita fola x \ariabili 



(fl):=,j,dx{fl\dvdz-^i\^))-Vdp<.ffVdydzM^)l 

 -^-dyi /fLdvdz-^-i''^)) U / /fNdxdydz^^)^ 



^dzUfmdydz^i^^^^^d/^f/V^dydz^i'^)) 



^dv{/f^dydz-\(^))-{-dp\fjV%dz-\-{'^)) 



^dci 



