DIFFERENTIO - DIFFERENTIALIS. 1 5 3 



colligi conuenit , haecque etiam eft caufa, cur eos non 

 flatim determinauerim. 



7. Quamdiu ergo x adhuc eft variabilis , et u 

 vt contos fpedatur , necefle eft, vt expreflio Riu+xf-* 

 aequetur huic formulae integrali : 



J?dx{u-t-x) n ~ t (-+ Auu -+-2 kux +An *} 

 -^nCuu -\-nCux -\-nBx 



-h«B« -H<*-x)D) 

 -4-«(«-i)F«« -i-«(«-i)E« 

 tcuius propterea difFerentiale aequari oportet huic: 

 (« -h *)"""*/» <*R -4- *<*R n 



Quia autem R ab « pendere non debet , conditiones 

 fatisfacientes his aequationibus .continentur : 



A-f-«CH-»(«— 1 )F — o 



dR = (2A-hnC)?xdx-t-n(B-t-(n-i)E) ?dx 

 xdR-\-{n-i)Rdx~A?xxdx-\-nB?xdx-\-n(n-i)D?dx. 



8. Si valor ipfius </R ex fecunda in tertia fub- 

 itituatur , habejbjtur ?. 



(n-i)R^z~-(A~\-nC)?xx-n(n-i)E?x-)-n(n-i)D? 

 et quia ex prima eft — A—nCzzn(n—i)^ y prodit 

 R — n?(¥xx-Ex-t-D). 



Deinde ob 2A-\-nC~~ zn(ri— i)F — «C fecunda 

 induit hanc fbrmam : 



dR~z n?dx(-(C-±-z(n-i )¥)x-\-B+(n~i )E) 

 quae per illam diuifa dat: 



dR -(C + a(ii- »)F) xrfjc -4-(B-f-(n-i)E)d ix 



R Fscx — Ex+D 



Tom. VIII. Nou. Comm. V vnde 



