2r^2 DISSERTATIO DE FROBLEMATIBFS^ 



§. 19. Frobkma V. Integrare aequationcm haneV: 

 adx-\-bdy -H cxdx -\- eydy -^fydx -{-gxdy — 0. . 

 Fadiim hoc quidem iam elt aliquot modis a lac. Her- 

 manno , iii Commentar. Acad, Jcient. Petrop. Tomo II. 

 pfig. I ; fed idem hoc problema breuiori via fequentem 

 in modum folui pofle exiflimo. Pouantur termini pes; ■ 

 dx multiplicati .a-\-cx~\-Jyz::u, nec nou termini ■ 

 per dy multiplicati b -h ey -\-gx — t :, obtinebitur 

 ibi y — " ■ " J-. ''^ atque- hic y — ^'^^^^ ; tum aequando: 

 hos duos ifalores, et breuitatis cauflli ponendo, 



deriuabitur x r:^ ai - ^ U -\- $; y :=z — y\ t-\-zu- ^^ 

 £t aequatio propofita mutabitur in hanc: 



a.u d t — ^ ud u — -v] t dt -\- £ t d u—: o, 



cft enim ob «7 -i- cx -\- f y ~ «, et b-^r-ey-^-gx-f^' 

 acquatio propofica />n/«(? talis, udx-{-tdy:=zo-, Qife- 

 imdo, dx — oidt — ^du ', dy zz ~y\dt -{-. edu, qui- 

 bus diffcrentialibus (iibditutis ia priori- aequatione emer- 

 §it propofua. Haec autem eft homogenea, adeoque 



artificio. . 



