DIFFERENTIO-DIFFERENTIALIS. 14J 



ideoque 



s_e jtqf — h d ) 



verum quantitatem u ex liac aequatione elki oportet. 



ddu __(c-^ex)du _, (f-\-gx)udx .^ . (ac-4-»,6cx-».& g_xjcyudf 

 d« jc(a-f.6*) ' x;c(a-f-&x) ""^ ««(o-+i-6«)* 



2 c 2 (d e .— li c) 



__C x^ {a~\-bx) «6 ~~<j?je 



■ — ■ i" 



4 « 



ct prioris quidem generls cafus liinc fumfa cbnftan- 

 tc C iz: o funt deduAi. Verum haec aequatio pofito 



— g e »1- b c 



« — :v« (^ H- ^ ;t^) «6 lu abit in haiic 



^^» -««v-t- ;c(o-t-6x) "^ xx(a-f-6x) 



cuius applicatio cfl: facilior, vnde fi C — o , quanti- 

 tas V fatisfacere debet huic aequationi 



(a ^ B x) d ii V '\-^'-^'=^^-^'''^'' ^ ^^-^^'^^'"^''' =L O 



ita Yt hinc ex valore particulari obtineatur com» 

 pletus. At fi ponamus u z= x"" (a -^- b xy- crit 



2 c j.ff, a fa<- ~&c)_^^ 



, V, .V « {,a-\-t^x) —-^nr + "xi^T^ 6 7) 



^i a(c-4- (3 — Fi)i>cy-t -( n— 1 )[nbb — be) xx 

 ' X X (a-i-b X)* 



ideoque tam eXponentes m tt n cum conftante C , 

 quam relatio coefficientium «, ^, f, e, /, ^ ex hac 

 aequatione definiri debet 



Tom. XVII. Nou. Comm. T 



