FORMVLARVM DIFFERENTIALIVM. 223 



d X — * dx 

 X 



ct multiplicator inuentus omnino ad priorcm redk. 



29. Propofita niinc fit formuln diffcrentialis : 

 ^x[ yy+Jz-^-z z)-\- dfz z-\-x i^x X )+ dz ( v x -\ xy -\-yy) 



et quia conflat eam non efie integrabilem , operam 

 darc oportct , vt inucniatur multiplicator , cuius ope 

 integrabilis fiat. Sit hic multiplicator zi (p>, qua* 

 propter , fi breuitatis gratia ponatur 



yy-Vyz-\-zz-\-p[zz-\-xz-Vx x)-\-p' (x x +xj -\-jy]-^ 



erit 



M = vp (^4)-^^^^"+ " ^*^^"^^'+ * ^'P'^ 



N - v^ (Jl) + Ct)(2Ki+p')+.vp'-fs); ?-(pixx+zz-\-xz^ 



g^ — vl^ (^^ + 4^C asf i+p)+A^+;') ; ^—4^. ArA"+.v>'+>y). 



Criteria igitur integrabilitatis quum nunc praebeant:- 



N - ^^ = o et !^ - 1» - o 



d X d X 



has binas adipifcemur aequationes : 



I- ^ (r>) - "A {xx-\-xz-\-zz)\-2(p{ y~x+pi{ y-z))-» 

 II. vP(J|) - 1? (.v.r+.t:r+j^}+2Cp(^-a4-p(^-r)j:=C7 



quarum differentia dat 



+2(|)(>'-;2Xi-hp+p')-a 

 conle* 



