-4^1 ) 52 ( ^fS*- 

 Corollarium I. 



§. "70. Hic notari meretur, iftum cafum adhiic 

 alio modo ex forma generali deduci pofle, fi fcilicet fu« 

 matur A n: o et E — o, tum enim prodit ifta aequatio 

 difFerentialis : 



L5 -f- ^ — o 



cuius ergo integrale erit 



■j^jx -hy)-h 2Cxy-i' Dxy{x -hy) ^ 7 V(Ba- + Cxae-4-r)r^UB'y-f-C:yj)+Dy) 



(x — y)^ 



— l_i — -?-, vbi valor conftantis admodum fim- 

 plex euafit. Nunc in his formiiis loco x tt y fcribamus 

 XX tt yy t at vero loco literarum B et D fcribamus A 

 et E, fictque aequatio differentialis 



d_x I d y Q 



VtAH-C^c^-f-Djcv) ■^[\-hCyy-h'Ey') 



cuius ergo integrale etiam hoc modo exprimetur 



^{xx-hyy^-h^Cxxyy-k-^Z x xyy (a x-t-y^) ip 1 x^ V X V _A_ 



Ixx — yyf' k k 



Corollarium If. 



§. 71. Ecce ergo hac ratione peruenimus ad alw 

 %m integralis formam non minus notabiiem priore , atque 

 adeo nunc ex earum combinatione formula radicalis V X Y 

 eliminari poterit , quandoquidem ex poderiore fit 



~ xryvi. kkxy xy *' 



- Exy (x x-{-yy) 

 qui valor in priore fubftitutus condacit ad hanc aequa- 

 tionem rationalem: 



2A + ^Cxy -^ 2.Exxyf 



,A(x-_2f ^:?:, «(;:— y)'VA.K — ..^^- - 



quae 



