FORMVLARVM DIFFERENTIALIVM. 215 



certum cft cam integrabilem reddi per hunc mnlti- 

 pliciUorcm Sy-\~Tp et ipllim quidem integralc 

 tum crit : 



quod pofito C — o , in hanc fatis concinnam abit 

 formnm : 



T T rt'/' + 2 T S}' dy dx-\-yy S S dx" =: B T dx\ 



25. Tribuamus iam mnltiphcatori Cp huius- 

 modi formam : 



(^ — Kyy-^Syp-k-Tpp, eritque 



(^^)=2^R+pS;(lf)=2pT4-7S 



/'ddCP^ dR , ^dS. ( ddCp S_ ^^dj dS 



/d dOJx , p . / d d 4> \_c . ; d d (|) ^ — o T 



^di;^;— 2^? Id^-dp/— '^' \-r^i — ^- 



His valoribus in acquatione pro criterio intcgrabiii- 

 tatis all.ua fubrtituiis, iitque terminis feorfim nihilo 

 aequatis , quae produdlis y\ y p ^ p\ y q ^ p q affi- 

 ciuntur , (equentcs confcquemur aequationes : 

 L ^.Kh-d.\^t—-\-'^-J^^^o 



^ d X * d X- 



"•+."- = ■/■ 



d d 5; 



d X ' li j:* 



III. 4R-2(SK4-TL) + J|-:r:o 



IV. 2R-(SK-i-TL)4-i^^-i^4-^^T_^ 



V. 3 S - C> T K + 2 ^-I- = 



Harum 



