AliaSolutio. 



5) Solutionem hanc, ctsi operosfor sit praecedente, 



ideo potissimum hic subjungo^ quia substitatio in illa 



adhibita viam mihi aperuit intégrale alteiiiis formulae in- 



vemendi. Posito x rr: —77— erit z izz. ~ et 



1 — XX ~\- 1 '\/ {\ -\- xx) 



%Z 



XX 



Hinc 1 + zz — -O + ^'-^x) ^^ 



1 — zz z=: 2 (■ + ^'C'— ^x))V(i— X.T) 



XX 



et diffeientiando 



^^ XXV(1 XX) 



Porro cum sit 1 + a;x z:z ^-4—^-^ habebîlur 



2^(14-/(1— XX) y^>^(H-a:x)\ 

 / ( 1 H- 6 zz + z*)5 — ^ 



Surrogatis his valoiibus in formula proposita orietur: 



1 ax/Yi +/(i +xx)) /(i — xx) 

 ay — _. ^ 1 i ^ . 



Y 2 X y ( 1 + xx)^ 



6) Pro tollcndis signis ladicalibns, nomeratorem in-, 

 'gredientibos, ponatur primiim /(l -xx) =/, unde obtinebitur 

 — a» __ _^_ ^ j^gç. j^Qj^ i7 (1 -^ x.t)3 =: y' (2 —7/)' unde fit 



(1— jr))^(2— //)' 



— — , erit 1 + r =:= V 

 nec non 2— //^^^^^^JL unde onetur 



Fiat jam / - ^, erit 1 +/ ^ ^I^T":^ et l -yy^'-^^^i 



