J3,4 DEMOl^STRJTIO THEOREMA'!^ 



vnde, ob^.~j, per x multiplicando oritur : 



d X du 



y{X—Cjjxxy-xv A(A-+-B/t-hCj ♦) A{3^>1i:^ 



qiiiie multipiicata pcr ^j (yj"-xx)y A praebet : 

 ^Vi^^^f" ct Vr^Conft.-h^ip. 



Quam ob rem pro formularum incegralium difFerentia^ 



habtbimus: 



f dy(^l-^^y' f dxl^J-^^xx) rr>nrt _J_ ^^^^ 



J v(ah-b>'j-+-cj*) J v:^-^&xx+-cx*) — v.onii. -t- VA' 

 quae ytique ett geometrice alfignabilis. 



Coroll. I. 



1 1 . Propofitis ergo duabus formulis integralibus 

 fimilibus 



rdy{Jl-+ -^y y) rd x (M -4-'^=^ x) 



J y(,v_j_B>j-|-C>'*) ^^ / V(A-hBj:x-t-Cx*) 



ciu^modi relatio inter x et y exhiberi poteft , vt ha- 

 rum formuhirumi difFerentia fiat geometrice afllgnabilis. 



Coroll. 2. 



12. Hunc (cilicet in fincm talis relatio inter varia- 

 biles x tx. y ftatui debet, vt fit; 



oz^i-hff-^-kixx-^-yy^-zxjV A^A-^-^^ff-^-Cf^^-Cffxxyy 

 cuius atquationis reiolutio cum fit ambigua , capi 

 debet : 



a: V A CA -f- B// -+- Cj^) -j-fV A (A >f- B J Xj±C_x*) 



y — A — CJfx X ' — 



- . ^, :>VA(A.+-B //•4-Cj*)— /VA(A -i-Byy -j-Cy*) 



et X ^ Cffyy • 



Coroll 



