$6 DE COMPARATIONE 



eflct E=zo, valor ipfius V rcmpcT al^cbraice cxhi- 

 beri poflet , \ti cx elcmciuib intv.grationis cft maui- 

 fcftum. 



2 2. Vcrum fi coeJTicientes b, c, d, e ctc. \t- 



cunque afliimamus, tum exprclVio / ^~ "^ /^V^ "<^'"^ 

 cjuidem fempcr algebraice cxhib ri pottnt ; attan.en 

 eius valor ahiorem qiiadraturam non iuujhiec, quam 

 in formula f ^m-^ .vT^Tfn) contcntam , quac proptcr 

 ea femper \el per logarithmos vel per arcus cir- 

 culares exhiberi poterit. Cum igitur fit 



X r= V/) ( A -I- 2 B .V -f- C .V .V -i- 2 D .v' -H E ;i'*) 

 ct Vpr/^ erit X = v^V(A+2B.H-Cv.v4-2D.vVE.v*) 



ynde inucnto valorc ipfius V habebitur fequcns in- 

 tcgratio : 



J V(A-+-:B;c_j_Cj:- + 2DjiJ+Ex») •r-J V(A-*- = B5-^-C>j-h;I)>' + Ej*; - VA * 



At fubditutis fupcrioribus valoribus crit : 



VA / ^'VlM-t-iDs-Hiiis) "^ j(EM-DD) • 



Exirtcnte j- — .vH-j'. Atquc hinc fcqueotia problc- 

 mata refolui poterunt. 



Problema i. 



23. Inucnire integraic comp4etum huius ae- 

 quationis difFercntialis : 



d y d X 



V:A-(-.B>-t-e.-v>-j--Dj'+Ej«) — V(A-t-:Bj:-j-C**-H;DA.'_j-£.<')' 



Solutio. 



