d*y -^ a/ d' y -\-^* d' X -A-y^ d d X '^-'^^ d dy ^sf d X 

 + <'«'/ 4- V *• + ^''j = o ; 



denotante nunc y quod ibi erat jr, et z qiiod ibi erat y ; 

 patet, coefficientes A, B, C, etc. in nonniillis terminis cuni 

 coeflicientibus ibi inuentis conuenire , alios vero pi-aeterea 

 ternninos inuoluere, qui ibi non reperiebantur. Sic pro 

 d^ y^ quod ibi efl: d^ x, fit 



C — 9^ + 3^(a-|-pO-f- 8(y -{-<^' )-|-e ~l- ^' 



quod praeter terminos 



£ ^_ ^/ _^ a a' - a'5 -i- 13' y - (3 y', 



infuper inuoluit terminos 



96-H3^(aH-p')-i-8(y-i-(J')-h9(«(3'-a^(3). 



Horum igitur terminorum formatio quomodo procedat , 

 nunc e rc eft "vt exponamus. 



§. 5. Supponamus igitur generatim binas ha? ac- 

 quationes differentiales effe propofitas: 



x^d^^y-^-ax^^-^d^^-^y-^f^x^^-^d'^-'^ •/'^^ ^'> 

 ^yx^^-W^-^y-^-^x^^-^d^^-^z 

 ^Bx"'-W^-'y -^ ^x"^-' d"'-'' z 

 -t- 7) jc"» - V" - ♦/ -h ^ a:'" - V" - ♦ 5; + etc. = o; 



x^d^^z-^a/x^^-^d^^-^y-^-^^x^-^d'^-'^ 



H- y' .v^ — ' ^f" - ^-jV H- <5' jc"" - ' ^^' — * 2 



H- e' Jtr^' - V" - ' / 4- <^^ A-™ -^ ^ ^Z'" - ^ 2 



-V- vi' jc*" — * ^^^" - ♦j' -1- e' jr"* "" * ^ 7 * 2: 4- etc r o, 



cx quibus aequatio differentialis fola difFerentialia ipfios j' con- 



H 3 tinens 



