CALCVLl VARIATIONVM. 75 



Coroll. 2' 



44.. Qiiodfi iam hic reduAiooes fuperiores adhi- 

 :beantur, reperietur eadem variatio ita expreffii : 



^/Z^^:ir/^.-^j((N)-g + S-^-2^-+-etc.) 



^^,((P).^+^).etc,) 



V£((Q.)-^S^^-etc.) 



-l-,S^((R)-etc. ) 



Coroll. 4. 



45. Cum fit ^=/W^5S5, erit A5B-58 

 ~f(^A-Wj2.dx-j quare fi ponatur integrale/ A-W.Sd^rrX, 

 ita fumtum, vt euanefcat, pofito x — o, tum \ero fa<5to 

 x=za , fiat X"B, ita vt fit : 



ygdf^xrrW, et pofito x^a^ fiat W— A, 

 /(A-W)£^:i;r3X, etpofitox — ^, fiat X zr B 

 fuperiores valores Coroll. 2. exhibiti ita fe habcbunt : 

 N-f-(A-W)g^-+-(B-X)llzz(N) 

 p_^(A-W)q3-f-(B-X)p:r;(P) 

 Q^(A-W)0-H(B-X)q-(q) 

 .RH-(A-W)3l-^-(B^X)l— (R) 



etc. 



Problema 5. 



45. Si in formula integrali Ozz/Zdx j quan- 

 titas 2 praeter litteras at, j, p, ^, r etc. ctiam ipfam 

 formulam integralem <D inuoluat, determinate eius va- 

 jiationem $Ozz$jZdx. 



K 1 Solutio. 



