§: iPy Si igitur fumto elemento df cGn^flante pro* 

 pofita fuerit aequatio integranda 



ddz + 2mdzd[-hnzdt*~(a(m.ct + lf'coC.ct)dr 

 ponatur dz — rdt, vt liabeatuc aequatio' differentiaiis pri* 

 mi gradus haec : 



dr'{'ZPirdt-\-nzdt—(afin.ct + cof.ct)dt , 



quae multipiicata per fundlionem quandam ipfmSi^f^ quae 

 £t T, fiat integrabilis ; fcilicet 



Tdr-^-zmrTdt-i-nzTi/t^zrzTdt^aCin.ct-hbcoC.ct) 



cnius membrum dextrum manifefto fit integrabile, id quod 

 igitur etiana in parte finiftra euenire debet, 



§. 2 1. lam vero perfpicuum eft integralis huius 

 partis finiftrae membrum vnum fnre Tr; vnde fi totius 

 partis* integrale ponatur n: T r -|- S, ita vt fit 

 T r -h S — /T d t ( a fm, c t -h b coC c t ) 



tum differentiando erit 



Tdr-^-rdT + dS — Tdr^-^mrTdt-^-nzTdt 



Tnde fit 



dS — -rdT-\-ti.mrTdt-i-nzTdt 



fiue ob r=^, erit 



dS--Vdz{'^mT-^;'-)-^-nzT dt.) 

 Cfuae forma euidcnter intcgrabilis redditur ponendo multi- 

 plicatorem T — e^\ denotante ^, vt ha(flenus , numerum 

 cuius logarithmus hyperbolicus n r, Tum enim fit 

 dS ~ e''^ [zm — ^h^dz^- n e^^ z dt y, hincque 

 S. ~ C -\- (, i m - X ) e^' z , ^ 



fi fcilicct littera X ita afllmiatur, vt flt zwX— XX = «' 

 hoc eft h —m-i-ymm-fr, lictera. C dcnotante conftan- 

 tem per integrationem ingrcfTam, 



§.2 2. 



