MAXIMORVM ET MI\nMORVM. 127 



termiiTim x—.a extenditur , maximum miaimum ve 

 vaioiem coiirequ.itur. 



S o 1 u t i o. 



In hnnc igitur finsm variationem differentialem 

 f()rm.il;ie /Z d x exqniri conuenit j quae cum fit 

 Sj Zdx~fS 2,dXy habemus primo : 



<5^Zrr .L^(|)-HN^jF4-P^/J4-Q.^^-HR(^retc. 

 ideoque \ariatio difFerentialis erit 



6JZdxz=.JLdx$cp+fHdxSyi-f?dx$p+/(ldx$^ 



~\~fRdxSrQtc, 



Nunc autem, ob $(^:izS f^^dx^zzj ^'^d Xy et 



§3 :z2o p -i- ^^ j -{-^^ p -hOJq -i-di^ retc. 

 habcbimus fimiii modo 



S^p—JICdx^Cp-i-f^dx^jy-i-f^dxSp-hfCidx^q 



-{-fdidxS r etc. 

 Denique vero eft d(f)=z$f^dx—fS^dx^ ideoque ob 



^Ji::n<5>4-pJp-t-q«^^ + V^retc. 

 erit 



^^^fndx^y-^f^dx^p-^-fqSq-hft^x^rctc. 

 Sit lam. j^dxrzzVy ac fiet 



j^d x^ (^ ~vjdx W^ y ^ ^S p -\-<\^ q^X ^ ^^^c. ) 

 "fvdxiW^ y-^-X^Bp-^-^^q-^-X^rtic.) 

 vnJc acqiiirimus 

 B <p sivid xiW^ y -\-^^ -\-<\^ q ~{-X^ rttc.) 



-^-Jdx 6y (3Z - V W) -Vjdx $p {^ -v^j VjdxSq^O^-vq) etc. 



Pona- 



