,^6 ;METHODrS ^CFRVARjm 



."vnde aequatio aflbmta huic^aeqnationi integrali 



f'^^J-r fatisfacit. 



30.'Sinc.Jam X,et Y futK^iones ipfarum -^a? .et^ 

 fingulatim , ac ponatur 



rXdjc f \ dy »r 



J V J "qT— ^ 

 ita vt fiat V quantitas algebraica : eritquc 



f X— Y) dx , y, -f-(X— Y)dx 



31- PoGto xyz^u^ vt fit dy~-^ ~"^ir^? erit.:? 

 ^a: [mxx — nyy) -H ^« (w/ -f- <J a") — o 

 ,vnde, cum fiat ^^^ = ^nrk^, .erit 



** ' mxx — nyy > 



.liincque non difficulcer ccafusintegrabiles eliciuntur. 



32. Sit enim primo Xrrw;cA:, et Yiri.wx^^rCtit 

 dVzn^du^ et Vzz — «z= — xy 

 Hinc relatio inter a: etj aflTumta latisfacit huic aequa- 

 tioni integrali : 



^^_xxa. ^jnyy^ _ ^^^^^ _^^^ 



33« Sit fecundo XizzOTWJt*, et Yi^rwwy*, «erlt 

 ,<? V — — du [m X X -\-i^yy^ — -\- du{a 4- 2 (5" «) 

 vnde fit N — u[a-\-]B u)zz-xy (ol-^^ xy) 

 Ergo huic aequationi integrali 



.mmx^dx rnny*dy /~< n. . / • -^ v 



J — p / — ^ — zz Conft. -I- xy (a +> ^y) 



/atisfacit relatio affumta inter x et/. 



r34-. flis 



