Solutio.

§.xxn. Ponatur summa hujus seriei, quae quaeritur ~j-,ut fit

_ i. i_l . r. u z _i_. 1 . 1 . 3 . 3 . j

2-2 2.2.4.4. 2.24.4.6.6

&c.

Jam eligatur series, cujus summa confiat, & cujus coeffidentes jamin his terminis contineantur. Cujusmodi efi haec

t y ( 1 — xx)

4 , 3-5 , i-3s-!-7 8

. I -T- 3 , XX ft" " 7 X + -—- X +

2-4

&C.

2 . 4.6

24.6.8

X +

Er# ergo per differentiale quodpiam dP multiplicando & integrando

s4r~ -x +1 sxxdP + dP + l ~^lsx 6 d? 4- &c.

V ( l — xx ) 2.4 2.4.6

Nunc differentiale hoc dP ita definiatur, ut si post integrationemponatur xZZZ I. fiat

sxdy

sx dP :

1 P

2 1

3 /ru'iP4

/r ip rz: 4- I A* 6

P

p

1.1

~~ 2.4

_ !iL*_32.4.6

sx a d?zz+{sx dPrz —

24.6.8

quo facto si hi valores substituantur habebitur;

p / 1 __^ _ r r l 3 _ r-l.r.Z .Z.5

2.2 2.2.44 2.244-6.6

/;

y (1 — •*-.*■)

- &c.)