crit hoc integrale poftrenum 



2A4-B (i x-+-i y — k) -h *C x,y + f\/ .^ (\ -KbT+ C fe fe _ 



aA4-EK4-tVA(A+Bfe-f-Cfcfe) 

 fefe 



vnde ftatim deduci poteft aequatio canonica 



Corollarium II. 



§. 54. Ponamus nunc efle A z: o et B — o , vt fit 



X-xxiC+Dx + Exx) et Y-yj (^C-\-Dj-\-Eyy) 

 et K^kk {C + Dk-{-Ekk) 



aequatio difFerentialis integranda fiet 



d X d y 



— O. 



X ■^{i.+l)x-+- Exx) y -^ {C-i- Dy -h£yy) ~~ ' 



cuius ergo integrale erit 



a: 7 f 2 C + P(x+ v)-4 - lEx-v l+i JCv V (C+P x4-E 3e x) (C-^-Dy-t-Eyy) — ^ 



atque hic conftantem A per k definire non licebit : po- 

 litio enim y — o incongruum iam inuoluit. Interim ta- 

 men et haec integratio maxime eft memoratu digna. 



Corollarium III. 



§' 5S- Qi-iod fi autem in hac poftrema integratio- 

 ne loco .V et y fcribamus ^ et ^ primo aequacio diffe- 

 rcntialis erit 



d y ^ jc o • 



V (Cjy-<- Pjy+E) V(Cx.-<: -t- Px-t-E) ' 



tum vero integrale fequentem induct formam: 



iCxy +^0 (X -^y) ± i 'E + ^ ^ (C X x-i-Tl X -h-E) (C y_J / -i- T> y -i- t) — ^ 



{y — x)^ 



P fe+j E j> i V E (C fe fe -H P jJJlE) 



kk 



Si 



