i€+ DE RESOLFTIOKE 



tum indagabitur , nequc in hoc modo p:ruenitur a<f 



n 



;OCX 



formulam integralem, cuiusmodi eft ca fe~t~~~adx:zz> 

 quae integrali completo , quod inuen ; mus , inuoiuitur. 

 Cum enim aequatio dy-\-ayydxzzzaccx 7n -"dx ma- 

 neat inuariata, (ine c affirmatiue , fiue negatiue, accipiatur, 

 babemus vtique duo integralia particularia , quorum 



prius eft yzzz?zzzcx n — I H~ a ~f"Jx> exiftente zzzzx * 



— yn- fr-i — S*-4~\ 



+ (** — ') * * , (nfi— 'Vpnn— i) x • ' _. # 



« n . al P" ~ ~ TT~- a*c* ~ CCC * 



Pofterius vero fimih rnodo inueitigandum erit yzzzQ 



-»n+« 



n — . . <*" /- - n-t-t (nn— i) * * 



zz~cx n — '4-aTd^; fietque a=.r-- ^-. ac — ' 



4-**5r^^ fcsr 1 etc. qui duo vabres » 



ct a tantum fignis inter fe differunt. Erit ergo tam 

 d?-\ a ?~dxzzz accx' n — 2 dx y quam dQ-t-aQdx- 

 ~zaccx' n ~~*dx. Ponamus iam R^Zq^^, quae ae^ 

 quatio fit integralis completa propofitae difrlreatialis ^ 

 quam formam ideo aflumimus, quia in ea vtraque par- 

 ticularium yzzz? et J—Q continetur , ilk ntmpe f$ 

 fiat R zr o, haec fi R zzz oo. Fiet ergo Q R Kyz? y^ 



... Q.R-P j L* J RRiQ. Qct R-R JQ .-RdP-KJP-+-Pcte 



hmcque jr R — , quae dat <//_ — uT_-7)* 



fubftituantur hic valores fiipn inuenti dYzzz — aV-dx 

 -\-accx' n "~~dx et d^zzz-aQQdx -\-accx- n -~ 7 dx t 



j »n— ,j . aP~dx QQ?Rdx , (P — Q.)dR; 



entque </> == * 6V tf n ~ ~dx-h j--; - -]-rr 4- <fT-7F 

 _r — a — jj^L — — - -4- tf f £ x 2 n 2 d r. fc.x hac aequatione 

 refultat iiaec (P-QJ</R=r-tf R</.r(P-Q)% quae di- 

 viia per R(P-Qj dat d ^zza[i^ r ?)dxzz-2acx n "- , dx 



