FORMVL. DIFFERENTIALIVM. 133 



Sit igitur integriilc ipfius ix^^'^dp confiderata q vt 

 conflnnte zzY^', et cliffcrentiale abfolutuni huius Y'^ 

 z^ ii^ dp-\-K^ dq^ inueniemus Tr''''!!:?!^ atque [^"." ) 

 — (t7-)» "^^^^e habcbimus k'^'' — k^^ -4- k^% pofito 

 quod K^^ 5 fit quantitas folam variabilem q inuol- 

 veus , tum autem quoque fiet 



At vero quum fit tam dY^' quam v^^ d q integm- 

 bile 5 erit quoque forauik n^"^ dp -^ vy^ d p integrabi- 

 lis , quin et adeo 



[kdx-^-ydy^izdp-^Kdq quippe quae erit 



^ ^ Y 4- ^ Y' + ^ Y^' -I- K^^ ^ ^, 



vbi quum fingula membra dY; dY'-, dY" ctK^dq 

 integrationem admittant , nullum eft dubium quin 

 eorum fumma 



zziJidx-\-ydj~\-7:dp']--Kdq 

 integrabilis fit , ipfo integrali exiftente 

 Y^- Y'-4- Y^^/K^^^^. 



4. Ad Theorema igitur laudatum lam pr§- 

 pius accedeis , confiderabo primam eius conuerfum , 

 quod ita verbis exprimi poteft : 



Sl pofitis dy — pdx; dpzrqdx; dqzzrdx etc. 

 V fuer,t eiumodi fun&io ipfarum x, y, p, q etc. iJt 

 fomula V d X Ji^t imegrabilis , tum pofito 



R 3 dV 



