i5tf DE CRITERIIS INTEGRABIL. 



9) = (f^') +p (^-f ) + q m + »■ (||') -+- etc 



P' iH) -+- ?' Ct^) +' ' ('-f ) + ^'<=- -^ '' 



ctc. etc. 



Hlnc autem multiplicando vtrinque per dx et in- 

 tegnmdo , confequimur : 



IK—f^dx; v—fNdx', v' — f^dx; 'nz=:f(P-v)dx: 

 m':^fC^-y'}dx; K—f{St-iz)dx\ R'-/(a-7r'y^v etc, 



16. Hi valores ipfarum (x, v, v^ tt, tt' etc. 

 adhibito fupra §. 4.. recepto fignandi modo , fic quo- 

 que exprimi poterunt : 

 \k-fm.dx', vzzf]<^dx; v^—f^dx; 

 rn—fVdx-f^'-^\>^dx', Tt^—f^dx^f^^^ridx 

 Kz:IQJx-j^-Vdx\-f^'^Ndx', K'-f£idx-/-^^dx+f''TM' 

 etc. etc. 



r:zfTdx„,.±f'^-''^Pdx'^f^'^'^Ndx; cr'=:fedx..., 



^f^^-^^^dx^^p^mdx 



vbi figna fuperiora valent , fi m et n fuerint nume- 

 x\ pares , contra vero fi impares. Vlterius quum 

 formula V d x differentialia vitra d t et d s' progre- 

 dientia inuoluerc nequeat , euidens eft fbre t ~ U 

 ct (j'—%^ vnde iiae deducuntur acquationes 



%-^^f^'''^dx±f^^'^''^dx'Tf'^''''OJx,,..^-f^d^ 



quarum prior poft ;;/ diffcrentiationes et diuifiones 

 per dx reducitui* ad hanc 



