(15) 



*• = 2 fin. Cf) cof. C|)* -h fin. zi: fm. $ (i ^"2 cof. $*) j 

 tum vero erit 



j — cof. Cp (i -{- 2 fin. Cp*) 



et arcus curuac 



j =: 3 fin. Cf) cof. Cf). 



Exemplum 5. 



§. 26'. Inuenire formulam differentiahm 9 ^, ^«j^ y?«tf 

 muhlpUcata fiue diuifa per datam quantitatem t euadat integra" 

 bilis, 



Hic ergo hae duae fbrmulac f 3 W et — reddi dcbenC 

 integrabiles. Pro hoc igitur exemplo crit p — f et ^ — f , undc 

 fit dp — dt et dq:=z — |i. Cum erga fit ^ = j^^ erit 



• p 9 q — q d p — 2 3f 



undc pcr p p zzz 1 1 multiplicando flt 

 pdq — qdp— — tiLi 



quae formula porro difFercntiara, fumenda d t conflans, praebct 

 pddq — qdc)p~-{-^^. 



Deinde quia eft |^ = — JL , fiet 



i p d d q — ^ q ap g dt 



quae aequatio pcr d p~ multiplicata praebct 

 dpddq-dqddp~miy 



cx quibus valoribus co]h'gitur fbrmula quaefitai 



a w — — f_i^ -_ I dv-i-^i 



fiue hunc valorem duplicando et figna mutando flatui potcfl 



a w = '-i^ ^dv—^^, 



d i t 



§. 27. Mukiplicemus igitur hanc formam per t vt fiat 



td 



