Dell' Accademia . <?p 



SCHEDIASMA IL 



Thcoremata ad Cihulum Integralem fpeSìantia . 



N Euleriano Opere abfolutifnmo De Calculo Integra- 

 li , in quo tot eximia , ac prope divina occurrunt 

 de Formularuni Logarithmicarum , oc exponentialium 

 Integratione, nec non de Integratione Formularum an- 

 gulos finufve angulorum implicantium , videtur aliquid 

 defiderarl circa Formulas illas difFerentiales , qu£E potcfta- 

 tem anguli duflam in fìnuni , aut cofinum anguli ipfius , 

 vel in ("mum aut cofinum Logarithmi anguli ejufdem 

 complc6^untur. Prafto funt mihi hac de re Theorcmata 

 fex, qu2 neque inutilia fortaffis , ncque inconcinna vi- 

 debuntur. Demonftrationes in pofterum dabo , a Geo- 

 mctris cateroquin facllJime inveniendas. 



THEOREMA I. 



y . x" dx Cìn.x = — %" cof. X 4- n x"~ ' fm. x +- n. ìi ~ i . 

 x" — ^ coi^ X ~ n . n — i . n — z . x"~i fin. ,x _ n . 



« — I . « — 2 . » — 3 . 3C"~+ Q0{.X 4_ 



n . n — i.?2 — 2 . Il — 3 n — m -i- 2 . 



f x" — '"■+-' d X Y^ \n cof. a:, fi terminus prscedens con- 

 tinet cof X , vel in fin. x fi antecedens terminus com- 

 pleftitur fin.'xr. 



Cor. Formula efl: Integrabilis quando n numerus 

 eft affirmativus integer . 



THEO- 



