FORMVL. DIFFERENTIALIVM. 137 



Qiium vero per hypotheriii fit 



dV-zzmdx-^-ndy-^-Vdp-^-Qjlq -^Tdt-^-X^dii 



habebimus hos valores jnter fe comparando 



Uzi:T/^"'^NV.r± ^^'""^l^dx^p^^^^Qdx,,. .+fTdx fett 

 p'^^Ndx-f^''"^FdX'\-f^'^''^(ldx.,.,^/Tdx±lJ-o 

 Tnde differentiando et diuidendo per dx, prodit 

 /^'"-'^N^.r-/^'"-^^P^^'4-/^'"''^Q.^^^....^=T + ^=:o 



atque poft m repetitas difFerentiationes et diuifiones 

 per dx 



d_? ddQ^ d^ _^^ ^U_ 



^""^a;"^77 " dx''^"'''^dx^-' — dx'^'-'^' 



6. Nunc vcro facile perfpicitur, quomodo haec 

 demonftratio in maius compendium redigi potuiflet. 

 Confiderantes enim valores coefficientium [ji,K,7r,K, etc. 

 inueninius eos hac lege procedere , vt fit 



'n—f{?-y)dx; h-/(Q— 7ry.vj ^=/(R — h)^a: etc. ,' 

 vnde terminus ipfum r infequens, quem nominemus 

 V hac aequatione exprimetur v-f([J—r)dx^ quum 

 vero obferuatum fit rdt efle in expreflione V dx 

 vltimum terminum , erit v:z:Oy vnde deducitur 

 U — r :=: o , fubftituto igitur loco r valore ipfius 

 aequatio lupra allata emerget. Denique et obferuari 

 imeretur , hanc aequationem U — r z:: o , exindc 

 deduci quod fit : 



Tom.XV.Nou.Comm. S U-r 



