A N A L Y T I C A E. 141 



i-\~z~{-zz coiiridcrauimus , quarum termiiii me- 



dii fcriem eonftituuut, cuius fumma eft ~ y^mrjTTS) , 

 Yti rupni inujiiimus. 



Problema 5. 



22. Formulam in praecedcntc problemate in* 

 ventam : 



n 



r > » — bz — V[r — i6z- t-(6 & — ^ac)zz) \ . 



V(" — 7bz-t-[bb — *ac}zz) { zaczz ~ ' 



in feriem conuertere, cuius termini fecundum digni- 

 tates ipfius z proccdant. 



Solutio. 



Sit breuitatis gratia bb — ^ac—e^ ac ponatur 



n 

 _ , / i o g V (i — ; 6z-4-ggz) \ 



•' — ^[i..tbz-+-ezz]\ 2 a c z z I 



quam relationem inter 2 et j- per diffcrcntiationem 

 ab irrationalitate liberari oportet. Hunc in finem 

 ftatuatur : 



l aczT^ — '^ vt fit acvozz-^x-bz^v-^-^-^ 



Ynde diflferentiando fit : 



dfDkxacvzz—^-^-b^i^-^-fOdz^iacoz-^-h) — ^ feu 



dvV {i -ibz-^-ezz)—'—'^! -Vii -zbz-^-ezzj) 



• i dv d z d z 



ideoque ^ =r ^v-r-^Trrj;r7^z) ~ T- 



Hinc iiia aequatione logaritiimice differentiata prodit 



d s d z[b - e z) n d z n d z 



S 3 Pona- 



