DE CALCULO IKTEGRALI. 151 



Quantitas abfoliita feriei /Jr -f- />' — h e(t .r ' j' ' z~% 

 hoc efl: ^^. Et quantitas abloluta huius aIK-\-lM eft 



Ambo hsec lemmata notiora (iTnt,quam ut demon- 

 ftrationejCuilibet in hifce yel leviter tantum "verGito fa- 

 cilime invenienda , egeant, fed tanquam fundamenta fe^ 

 quentibus erant praemittenda. 



Theorema r. 



Inte^ralis iequatlonu du zzR^dK, tjl iizrMR^"^^ 

 in qua M datur per aquationem bar.c dK— (^X-4-1^ M</R 

 4-R^M. 



Hanc sequationem difTerentialem in feqnentibus Ca^ 

 nonkam voeabo , quia revera regulam (iippeditat (ecun- 

 dum quam seftimatio litterx M tuto inveniri potefl, 



T)em. Differentiando sequationemM~MR^"^',fif dit 

 -fX-f-OMRVR-l-R^^VMzzif^-X-f-i^M^R-i-Rr/MjR^ 

 vel propter (hyp) dK—(\-\-i) M^/R-i- RJM„ habetuv 

 «///— RVK.Q. E. D. 



Theorema, 2. 



IntegraJis £quat onis du — R^S^r/K ^ efi u— MR^"*- ' 

 S'*"^', & (Cquatio Canonica ^K— (XH-i) MS^R-f-({jL-i-i) 

 MR^S-hRSr/M. 



Bem Aequatio ^— MR^"^' S^"^' differentiata prae- 

 bet^//=r [/X-|-i;MS^H-(|a-f-0 MRr/S-}-RS.^M)l ^ 

 S^ ,hoc ert propter r/Kz=^X-f-i;MSr/R-H([M-t)MR^S-H 

 RSJxM, fitrf//— R^^S^^^K. Q. E-D. 



Theorema 3. 



Aeqmtio du:=zK^ S^Tdli.integralem habet f<=R^^-^' 

 S^-^'T''-^' M, cidus aquatio Canonica f/? </Kz=:(^X-f-i;. 

 MST^R-f-fr4-i;MRTJS-f-(v-f-t)MS.S^^T-hRSTrt'M. 



De- 



