244 DE INTEGRATIONE 



Eadem plane ratione , fi occurrat nequatio differen-- 

 tialis quinti gradus , in qua aequatio ( IV ). quinque 

 habet fii(flores , m — e z=r o^ m ■—fziz o, m — g -rz o, 

 m — i zz o , m — k— o atque fit i ziz k , inuenietur 

 eiusdem aequationis fequens effe integrale : 



— T((f-e) (i-/)-4-(ii:g)(t -g) -<- ( ?• -/)(;- g)) |. V_ 



ii~ey [i—j)- {,.g)^ "^ a{i-e]{i-j')(t.g) 



kx -kx 



vbi obferuandum eft, quod fit VnN «(E-f/N'« T</j»;), 

 quae fundio , vt fupra oftendi , in commodiorem 

 rcutari poteft formam. 



7. Qiio magis de veritate eorum , quae in 



praecedenti §. adduximus , conuincamur , fecundum 



methodum in §. 5 exhibitam examinabimus , quem 



valorem accip at j^ dum integranda occurrit aequa- 



tio differentialis quarti gradus , in qua duo valores 



ipfius m ponuntur aequales. Sit itaque a j> zz. 



A^ Q-4- B'' R -f- C S -^ D'' V , in qua aequatione 



coefficientes A'', B'', C'', D'' fequenti ratione indngan- 



tur. Dum j fucceifiue differentiatur , fequentes 



inde oriuntur aequationcs diflferentiales : 



rj^x' — ^{ A^Q4- B/R+CS + D'' V ) 



qadjdx' —'Jf{e A'Q_-{-f B'R+{g C''^ a DOS+g D^V) 



ca^ddydx' zz ^-^\/A^QH-/'B/R+(g''CM- 2tfg DOS+g^D''^) 



h. a^ d^y d X - 4^^X/A/QH-/^B^R4 (g'C^+3^/D0S+g'D/ V) 



a^d^j-i^{e'A^(^f^^R-^^[gX'-VAogVi^)^-Vg\y^) 



^y^dx\e k'-\fW -^-g' Q' \:>,ag'D\ Nam 



