ET SOIFTIO ?ROBLEMATIS. 133 

 Pro hoc ergo cafu erit : 



et y ( A -H BxK -i- Cr) zz z:^=£fjyy)±^^)±^r_±c£ 

 iicque fiei : 



f dy^ S. ^j ' /d x_VA 



jyA(A-+-Bf/-t-C;*J— :c(A— C//J)') "1" aVA(A-+-B// +Cj ^)-j(A-C/j;c;c) 0' 



Lemma 2. 



10. Eadem manente relacione inter binas varia- 

 bil^^s X ctx vt fic o—-Aff-\-lK{xX'\-jj)-ixyVX 

 [A^.Bff-±-Cp)-Cffxxyy) , feu 



jeVA(A- i -B//-f - C j*}-i-J V\[A-i -Bxx+Cx*) 



y — A Cffxx 



yVACA-f-B//-t-C.» ) -/V A( A-t-B^j>-(-C7- ») 



et A: A. Cffyy ■ 



erit diffe^entia harum formularum integralium 



/ VCAH-Bjj -i-Cjy*) ~ J V (A-f.BFx^-Cx;*) 



geometrice aliignabilis. 



Demonftratio. 



Ad hoc oftendendum ponamus hanc difFcrentiam 

 ^V, \t fit: 



VCA-t-Bjjy-HCj*; V(A-hBj:x-+-Cx*) — "^ 



>^ ^ d 2_ _ d X . 



Vjjliare CUm llt ^(A-f-Bjyj-f-Cj*) V(H-Ba: -hC;l*J» ^^''^ 



jy g6(37--!C£)dx ?5/fjy j— x^;a. V A 



V (A-f-BJCJC-f-Cx*) — > (A— -C/Mx)-^WA(A-f-B;/-»-C/V" 



Ponamus iam xy — U^ vt fit j/::!:^; et 



o=:-A/-{- Aa^x-+-V^-2«yA (A-|-B/-4"C/*)-C/«« 

 qua aequatione difFerentiata fit : 



o-kxdx-^P- -t- "^^-diiV K^^Bff-^CryCffndw, 



R 3 >'i^<^e 



