134 DEMONSTRATIO THEOKEMATIS 



Coroll. 6. 



7. Viciffim ergo fi Iwbeatur haec aeqnatio dif^ 

 ferentialis : 



dy , dx 



■•(A-t-BjjyH-Cj*) ~T- v( A-f-BxX^Cx+) ^ 



relatio inter x et y ita (e hibebic , vt fit : 



—a:VA(A- 4-B/f-f-C/*)-t-/yA( A-4-Bj;a:-f-Cjc* ) 



y A Cj/xx 



f -:y V A(A -4- B ^/-f-C/* ) -h /'V A(A +■ Byy-j- Cy* ) 



leil a — A.-Cffyy 



Coroll. 7. 



8. Verum propofita hac aequatione difTerentialii 



dy d X _ 



V^A-t-B^jy-H Cj*) ~ V(A-j-B;c:c-(-Cx*) ^ 



aequatio integralis compieta erit : 



a:VA(A-f-Bf/- f- C/»)-f- / VA ( A-f- Bxx-f- Cx*) 



J K-Cffxx > 



r *-. — j yVA(A-f-B//H-C/*]— /VA (A-f- B jyjy -f-Cj*) 

 leU % — A C//J7 



S c h o I i o n. 



9. Retinebo determinationes huius poftremi ca- 

 fus , quibus efficitur , quod fi relatio inter binas \aria- 

 biles ^ et ^ fuerit 



r. 3cVA( A-f-B// -f-C/*)-f-/V A(A-f-Bxa:-f-C3:*) 



luie ^— A-rc7/Tr 



-^ -, j/VA ( A-f-B//-4 -C/^)— / VA(A-f.B jy7-f-Cj*) 



tum hanc aequationem differentialem locum habere: 



dy_ d X 



V(A-J-Bj7-+-C:y*) ~~ 7(A4-Bx jc -f- C x+) — • ^ I 



fcu fumtis integralibus fore j 



Ay _ f dx_ Cc\r\(^ 



V(A^Bjj-^c3*) ~7 V(A-i-Bxx-HCJi*) — ^"""« 



Pro 



