144 METHODFS CVRVARVM 



Atque erit cp:=zy:=z;jj^^ {-Vm{n-^\)-\-yn{m-i)) 



tum vero accipi debet c zr: a'^^^~^'}y 



Qiiae eft folutio fimpliciffima Problematis Hugeniaai. 



Solutio fec unda. 



105, Cum relatio inter x et j fit ita compa- 

 rata, Tt fit 



V((n-4-. )yy^cc)^ y^l{n^ ) ^ [m^ - i)xx , x _/, 



Ctqne U.x-i- :-f,»^' (0 ,-- e .) =r '^ '=i^,-t^. 



( naj' ^(''^ -t- i)yy — cc) aaeV{(n-t- t)ee — cc) ^ ccx V(aa -t- [m— ' )xx) ^ 



Capiatur in conoide noua ablcifla cqzzz, et pro ^ iam 

 fumatur jK, vt fit 



V(( i-f- 1 ) zz— f c)-+-z V(n-H . ) V/ T _i ( "'— O^J C , _j_ ^ V / «, t \ 



V((7i-+.i) jj_cc)-+-j^V'(nH- ) ^ [^ ^ aa J~T~a »'^'»-•1; 



erit pariter n..t + "j^^^'(©.-0j)=:'^±i), 



/ aazy( (n-H») z; — cc) 0^7 V ((>;-f- ,)yy ^^cc) . ccxVia -'- h(m . )xxK 



V(m— -J 7(^1^^ ■" V(i-t- 1) '* 



io<J Addantur hae tormulae inuicem , atque y 

 prorfus eliminabitur ; fiet enim 



iS??^ljt:*tT; = ( V ( r + <^"-') + ^5- y(«-,))- 



eritque: .n.x -+ ^-f^^S^-fjVe^ -0O=:=^^x 



/ aazV ((>z-f-i )zz — cc) aapV(r t-f- i )ee — cc) ^ iccx-\f{aa-+-{m-—i!jxx) 



\ V^""— -^{m — ,} -~r- ~^ijrZi- ,) )' 



107. Statuatur iam 5^43l!_±j.'=s,feu..= :-^L"l:j 

 crit per — multiplicando 



Sup BIVH-Sup en-^^J-^-^ x 



/ aa2V((n-f- 1)22 — cc) oaf V((t h- i)ee — cc) ^ 2ccx^/iaa-+- [ m—i)xx) i 



*> V |m — I) V (TH '+" y (n + i) ' 



vude 



