ET SOLVTIQ PROBLEMATIS. 135 



Coroll. 2' 



13. Quemadraodum hic j per x et /, atque x 

 per y tt f definkur , iia etiam limili modo / per X 

 ct / definiri poteft. Erit enim 



j- j V A, (A -4- B 3c 3g -t- C X*) — - . jg V A (A -h Byy -f- Cy *) 



J — A Cxxyy 



vnde patet , fi fit xzzo, forejirr/, ex quo cafu con- 

 ftans iila, in \alorem ipfius V ingrediens, definiri debet. 



Scholion. 



14. Simili modo demonftrari poteft , etiam ha- 

 rum fbrmularum integralium difFerentiam 



J v[A-f-Bxy-hC>'+; ' V^A+B;cx+Csc+)' * 



effe geometricf aftignabilem : Pofito enim xjzizu erit; 



d^^-^j^iTi^r^ '25' yy-xxyvilir-x^^+^^iy^-x^xdtoc^MQ 

 dV-^-^;f^)^-\-(l{yy-^xx)~\-<7),y^-\-xxjy-\-x')) 

 At ex aequatione canc nira habemus : 



A// -f- 2uV A (A -4-B //+ Cf*) + C//u U 



A^^v-l-jji^. 1 



Ponamus breuitatis gratia V A(A-i-Bj-}-C/^)-F^, vt fit 



A.';r-hj7 — ^(^'^"i-^ ^u-\-Quu) , 

 eritque ob j/*H- x xyy -4- x* =: {X x -i-yy) -uu 



ideoqne integrando : 



v^ / y^ /-l-^rA«-i-F«f^-^iC/^n-l2)^'^' 1 



'^K'!ir^^A«i-2AF^<«+|CA.C4-2FF,«'+CF«*+;CCrf 



Verum 



