--^:i ) 38 ( ^?i<- 



quo fubftituto aequatio integralis erit 



» A + B (x +y) 4- C (x« + >») -f- D a; y (x_^y j -f- « E «'>* .4, > V X Y * 



§. 40. Haec aequatio aliquanto concinnior reddi 

 poteft fubirahendo vtrinque C et ftatuendo a — C — F: ha- 

 bebitur enim hoc fadlo 



vnde deducimus 



«i'L z:VXY-T{x^yy - a A- B (.v 4-^) - 2 C a-/ 



— D xy (x-^-y) —^'Ex xyy 

 Cue ponendo 



2 A-f B (jr +^) + 2 C xy-^^Dxy {x+y) -f 2 EA-A-y/z: V 

 aequatio noftra erit 



a y X Y — r {x — ^}* — V , quae fumtis quadratis 

 abit in hane : 



j^XY — V{x ~yy - 2 r V (r -yf -h V V fiue 



4. X Y -V V = r* (jf -yY - 2 r V (a: -yf 



* 



§. 41. Fada nunc fubftitutione erit 



4XY ~4A' -f-4AB(jr -hy) -H 4 A C {xx-Jtyy) 

 4- 4 A D {x' + j') 4- 4 A E (jf* + j^) + 4 B B jc/ 

 4 B C a: ^' (j: 4- J') -f- 4 B Ti x y {x x ■+ y y) 

 ^BExy{x' ■^■y')-^- ^CCxxyy 

 Ar ^D x X y y {x -^-y) -\- ^C Exxyy {xx+yy) 

 -j- 4D D x'y' + 4 D E x'y' {x -\-y) 

 H- 4 E E x^y*. 

 ht vero porro colligitur fore 



.VV:zr4AA+4AB(A- 4- j) -f- 8 A C atj' . 

 -\- ^AD xy {x -\-y)-\-h AExxyy -\-hB{x-\-yY 

 >W» 4.4B 



