50 DE JEQFJTIONIBVS 



ctionibus ipfius x\ erit d 'zzzzT dy ~\-y dT -+- dS his fiib- 

 ftitutis prodibit iila aequatio 



(tf+-&u n )TA* 2 ^+-(tf+-/>^ 



-(c-\-fx n )Txydx ~\-(c-hjx n )xSdv 



■z{a~\-bx n )x z T$ydx -\-(a-\-bx n )x 2 S*dx 



-\-(g-\-hx n )dx 



ex qua , quo terminus y continens egrediatur , ponatur 



(a-\-bx n ) xdT-\-2 (a-\- bx n ) xTS dx -+- (c-\-fx n ) T dxzzzo , 



dT „ (c-V-)x n )dx 



feu tft -+- 2 S dx -+- ; — - -- — j — "zzo. Ponamus ante omnia 

 T («-+•/? .v"; x 



i £zz-X&\ quo poft diuifionem per (a-\-bx n )Txx coeffi- 

 ciens ipfmsy^v fiat fimplex poteftas ipfiusv; erit -£ - -+- 



r-+-/^ -c-ap-(f-\-bp)x n 



aS ^^P^>= atc i ue s = — i*x«-t-**i — : 



Hinc iiet dSzzza(c+ap)dx-a(n-i)(f\-bp)x n dx-\-b (f+bp) 

 x 2n dx. -\-b(n-\-i)(c-\-ap)x n dx 



2 X x(a-\-bx n ) 2 

 Atque his valoribus iiibftitutis obtinebitur ifta aequa- 

 tio { a -+- £*") v^Vj -+- ( a -\- bx n ) x x - , "+" z j'dx -+- 



p (p- \- 2)( a-\-bx n )dx (c-\-2g)dx -\-(f-\-2 b) x n dx 



" +- • 



~-ccdx-\-in(bc- af) x n dx - 2 cfx n dx - ffx 2n dx 



-f-+u t T'_ = " qme 



per (a-\-bx n )x-'~* m2 diuila reducitur ad hanc dy-\-x*y~dx-\- 

 p(p-\-2)dx ( c -\- 2 g)dx -\- (f-\- 2 h ) x n dx — 



+V*-*- 2 j ^(^-i-^.v 71 )^ 2 



(c-\-fx n ) 2 dx-\-2n(bc-af)x n dx 



— f^+i"^ ^ iae ae 9 liatio ita eft com P 3 * 



jata , vt pbfito gzzz— cm-am(m— 1) et hzzz-fk—bk(k—i) y 



fcm- 



