ts± SOIFTIO PROBIEMATIS. 



prodibit dy zz udx-hxdu rzp dx Vnde rrj == f > e * 

 aequ.itio prnecedcns. mutabitur m lequentem — p— ,»« 

 ~[u — p)*xx, «umendis logarithmis fit /^z^-+-/(i+p/>) 

 zz.±Au-p)t*lx, et difFerentialibus ^p^-f-i* 

 Hinc ob — - = d a - prodibit i-t-p«~o» q«od ob 

 pzz~ et »=:-£ poft mtegrationem dat *#+jy=Conft. 

 quod manrfefto eft ad circulum abfciffis a centro com~ 

 putatis. Pergit Eulerusi 



7) Aequatio , W+w ^, w |.= fiB«§aS*l 

 porro per iubltitutionem y-pxz:uV(i -\rpp) hanc fup- 



peditat aequationem rr+£Z^jj = y(77^rino> iam c0 - 

 nemur omnia per nouam variabilem determinare , at 



ubftitutio afTumta dat per differentiationern (LJatiz:^ 



V{ i +pp) - vtK-pp)- Vnde oritur ob jqP*+ aV ( * +#>)• 

 {V)yzz- p ~V(i-±pp) + j~$. Statuatur porrcv 



breuitatis gratia ^^^ zznV, eric aequatio pro curua 

 ^&=V, fainc ^+^=^-^(1+^)+««, 

 ex qua reftat , vt j5> per u vel U determinetur , tunc x 

 ct y ex (C) et (D), per f >hm vanabilem exprefla ha- 

 bebimus: Cum igitur fit -ji i(i-\-pp)-\-uuzz. — ^t5~~ ^ 

 ffatirn 



dp dU V '(i_— U ) 



\-*~p"p — V(aaU — oi— uu(i — U)) 



Si pro « ex antccedenabus valor pcr U expreffus fiib- 

 ftituatur , aequatio fepsrata integrari poterit per fignum; 

 fummatorium. Hinc p innotefcet perU, ideoque etianii 

 per itj et problema erit lolutum. 



