AEQVATIOKIS. i 57 



Haec crgo expreflio generaliter in infinitum excurrens 

 fit finita , fi fuerit ( _ i -i- 1 ) a »« — i =_: o , denotante i 

 numerum quemcunque integrum , hoc e(t , fi fuerit 

 *—_!§__ J et w:_:_»--__:^^=^- 2 . Huius ergo 

 aequationis , quoties i fuerit numerus integer : 



— *i 2 ±2 



dy-\-ayydxzz:accx *'-*-< dx 

 integrale (emper in terminis finitis poterit exhiberi , 

 feu valor ipfius y per x algebraice exponi. 



Sit primo nzz-j~ t , vt fit m—zn- 2 = ^ erit 

 huius aequationis : 



dy-hay ydxzzzzaccx 21 -^ 1 dx 

 integrale iri terminis algebraicis expreiTum : 



ayxzzzzacx 2 l ~*~ l 



v 2 Z-f- _ v2 Z-f- r „2 i_f_ 1 



- _j _____:_• _ • __rj _?-•>»* _i_____:____sk£ ___. 



V 2M-i Y 2i-+-i ..Iwk 



t _ ______ __ _____ ^C_____)C ?-*-__) _ __!rl__i-__(ii_ )•____. _____ At/. 



1 a(zi-t-j)' ac "t~_.4(_H-i.*" -*- 2 -.4..(2Z-f-') 5 e*c» "T" ClC « 



(eu ftcl:a ad communem denominatorem redu&ione 

 erit : ay x~ 



2 /-f-i V 2i-r-i r 2Z-f-l 



acx --_-di).____X___)C ._____________!•_ _»_ etc 



_l__-4_. "T .._f_z___k_" -ac _._.rf_i-*-i)* «*c* "T" crc « 



v _z-f-i V 2.-f- x v .z-f-' 



i{i+__).* T ,*___J__H A _____*____!___ l Pfr 



*" sl-i+i. ec~~ T_. 4 ( 2Z4 - J )2 , -^i _T7(2/-t-0 5 * fl 3 c* "T ctc ' 



V 3 Sit 



