•44S ) »8 ( l?l^- 



qjuae aequatio per c u-^ a diuifa du(n:aque in c praebet 

 -—^ — r — cg, iiocque modo nadli fumus differentiale 

 logaritlimicum. 



§. i8. Dein vero aequationes principales vt ante 

 differcntiemus, et obtinebimus 



ddx Y/pt'^'^'^ — _Y' 



quae inuicem additae dant 



^fid^^ddy_s^X'-Y'—ticg', 



d t ^ dx * (X y ' '' 



quare fi hinc duplum praecedentis aequationis fubtraha- 

 mus, remanebit « 



1 / ddx . ddy icdu > ^ 



d~t ^ d w ' d^ cu — a' * 



Tnde per d t multiplicando et integrando nancifcimur 

 ldx + ldy-2l{cu-a] = lC, ideoque jA^y—-Cdr, 

 Cdrti igitur fit d x—X d t et dy — — Ydt, aequatio in- 

 tegralis noftra erit — ^ ^Za)^ — ^- 



§. 19. Per hanc ergo analyfin deduAi fumus ad 

 hanc aequationem integralem aequationis propofitae: 



(c-4-2&a:-t-cjcxl (a-^rby -+ - c J y ] Q 



{a —cxy) = 



quae aequatio, fi vtrinque vnitas fubtrahatur, reducitur ad 

 hanc formam : 



iab{x-i-y)-haclx-i-y)'-i.*bbxy-i-ibexy(x-hy') /^ 



" (0 — cxy)' 



§. 20. lUuflremus hanc integrationem exemplo, 

 ponendo flzr 1, bzno tt C — i, ita vt propofita fit haec 



aequatio differentialis: -^ 1 ^— o, cuius integrale 



nouimus effe A tang. jr -h A tang.j' — A tang. ^^^t2. ^ C, 



ficque 



