AEQJ^ATIOIUS. II 



tea, ponendo dy:=:zdx , hoc pacfloenim aequatio A a« 

 bibit in fequentcm adx -^ bzdx -\- acdx -^fxzdx -\- ejdx 

 ^-^r2;^.v=ii^-,quaediuiribilis eftper dx, etprodibit aequa- 

 tio d-^-bz-^cx-^fxz^ey^gyz—o, ex hac vero elici- 

 tur aequatio L. . . -4-.r==-( -^^eA-l^^-h-e^ ; hinc ae- 

 quatio differentiata praebet, dy[zdx)=Zl^±^^^^ 



{Cg-ef)xdz [ag--he)dz 

 ; r- 2 



haec vero rite reduda , fuppeditat fequentem aeqiiatio^, 

 nem M,quaeintegrabilis ell,M. . .^zr l^?zia_^^ 



{a g—he) dz 



'nr {gzz-^ez-^c ^x{gz^e)x 



I 5. Ad conftrudionem eius ponamus 



aP^ ^ ^S~ef) dz pnfnnp ^""S-he dz) 



P —igzz-^p-hc ^xfgz-^e^j^^^^^H^^ Jg^^ez^xfg^fy 



:=7|EiiVp~5 ^^^^ ^^^^^ ^^^^ aequatio M, abit in hanc 

 aiteram^__-p--t- ___p_, i^icaiur T^^z^p^ — ^ j 

 critque ^= p— }-^, et ex hac elicitur xzzpz^ , qui va- 



que ds.ziz^l=^J^/pj etfumtis integralibus Q=ia -f- 

 ^7^, hinc .v(=PQ)=aP+^-:^, et (.r+:f:^;)P- 



mconftanti a. Sed quidert P ? 



Eft autem [£I~^^) l^ .^P\— g^^^ , /3rfg 



gdz 



gz- 



ubi funt /— i/(^^^2f/l4-^^rg), jnzn^e 



Ipfa vero binomia gs-h?/2 et z-^-n , funt bini fa^fcores 



B 2 tri- 



