AEQVATIONIS. j<T 3 



zzzaccx 2n ~~~ 2 dx efife yzzz?-\-v, quo valore loco y 

 fubftituto habebimus hanc aequationem d? + dv-\a¥dx 

 -+- 2a?vdx-\-avvdxzz:accx 2n ~~~ 2 dx. Cum vero 

 fit ^P-4-*PV# — tf^.v 271 -" 2 ;/*, erit dv-\-ia?vdx 

 •\-avvdxzzzo. Sit tfrjL, erit du-za^udxzz + adx, 

 quae inultiplicata per e~~ zai?dx denotante e numcrum, 

 cuius logarithmus hyperbolicus eft rr i , fit integrabi- 

 lis ; erit fcilicet aequationis e—~ aJJ>dx (du— za?udx) 

 zzze-' af?dx adx, integrale e--- af?dx uzzzfe- 2af?dx adx: 

 ideoque uzzze 2 afpdx fe— 2afpdx adx. Quo valore cum 

 fit vzzr. j fubftituto, erit integrale completum aequatio- 



e — 2 aJ? dx 



nis propofitae^-P^j^j^jp^— . At ex pro- 



blemate primo eft valor ipfius y particularis, quem hic 

 ponimus P \zzz, c x n ~~ '* -+- *^fe~ exiftente 



_n-fri — zn-t-3 -sw-f-* -?n+j 



. 2 i (nn-Q y a . fnn-i)( P nn-,) s » ( nn-t)($nn-i X^nn -Q rc _ 2 . 



* e n ' ac ~* an kr ' o 1 c 3 •" «n. isn. 24" 'a~c* -r etCt 



n 

 n — 2 acx 



Hmceritf?dxzzz c ^~\- a Iz, et e~- 2aJPdx zzze* n : 3,3. 

 Quo valore fubftituto habebitur integrale completum: 



n 



j — i acx 



j=cx—' + — y x -+ — 1 0: E> L 



u ^UX — -,acx 



zzje n adx-.zz 



Aliter. 



Quemadmodum hac ratione ex vno integrali par- 

 ticulari inuenitur integrale completum , ita ex duobus 

 integraiibus particdaribus expeditius integrale comple- 



X a tum 



