§, 57. Gum igitur ex aeqnatione fecunda flt 

 12 ii d (p = {s ^l-K) {3H d r coi', (p - s d d (p) , 

 fl valorem modo iuuentum fubftituamus, liab^bimus 

 12 dd(p=:-ssdd(p-idd(P-\-lsd(P' 



-f- 3 2 j ^ r cof. (p-^ i6df- fin.(p fiue 

 ('/ -f j i) dd(p-lsd(l)' + 3 2 j rf;' cof. Cf)+ i(J^/*fin.Cl5') , 



qiiae aequatio, vti ex praeccdentibus colligere licet, integra- 

 bilis reddetur fi per 2 d (^ multiplicctur j prodibit enim 

 z[%' -i-ss) d(pdd(p- s d(p' 



— ^2dt' (2 j ^ Cp cof. 4) 4- </Cj)fm. Cj)), 



\bi in fecundo membro loco d (^ fcribatur —zds^ vt ha- 



beatur 



[^l -i^ s s)2d(^d d(^-\- 2sd s d^^'' 



~- 3 2 r/ /' (2 j- ^ Cp cof Cp -i- <s? Cp fin. Cf)), 

 cuius intcgrale manifcfio cfl 



[\^ -\' s s) d (^' — ^2 d f- (- cof (^\-2fsd(p cof (^). 



Efl: vero 



/j</(I)con Cj)~ j fin. (^-/^^fin Cj) 



— i fin. Cp 4- L /^ Cp fin. Cp rr j fin. Cp - • cof Cp, 

 confequenter aequatio nofira integralis erit 



(V + j j) </ Cp'- =r 64 </ f [s fin. - cof Cp -f- C). 



§. 68. Quoniam igiiur hacc aequatio differentia- 

 lis cfl primi gradus ct diias tantum variabiles / et (|) com- 

 plcditur, pioptcr j-r^ — lCp, hinc loluiio per quadraturas 

 abfului poterit: erit cnim 



/fin.Cp-cofCp-^ C 



Hic 



