A N A L Y T I C A E. 135 



V~ ^ \-\^. }jl: V cuiiis intsgratio pracbct 



X z:: 



quae cft ip(a fumma lcriei propofitae in infinitiwn 

 coutinujtue.- 



Coroll. r. 



1«;. Liquet crgo ferici huius fummam cffe 

 imaginari:im nifi fumatur x<ii, cafu autem x~^ 

 fieri infinitam. At ipfi .v valorcs ncgatiuos tri- 

 bucndo, puta .vr-j, lumma fit finiti fumcndoj' < i, 

 at cafuj^ I imaginaria euadit. Ita ftatuendo x--i fit 



Coroll. 2. 



i5. Nunc ergo nouimus fcriem noftram quo- 

 qne refultare d formula irrationalis (i — 2A'— 3 .va*)"» 

 more folito in feriem euoluatur: qiiae formula cun» 



ita repraefeutari poirit sz=:{i^i—xy—^xx)'^'»* 

 prodit : 



■f — , — at"T~ 1 •(,_!)»+ ,. ,• (, _;c)*"r,. 2. ,• (, _*/ + CtC 



ex cuius vlteriori euolutione oritur : 



/ zr 1 4-Af H- Ar*-4- x'-\- x^-h a:*-H a^* -|- x' -^ x' -f- A''-f- x'* 

 H-c.i + 2.3 + 2.(5-1-2.1 0+2.1 5 + 2.2 1 + 2.2 8+ 2.35-f-'>.. ^5 



'i-(J.i+-(>.5+5.r5+-(J.35 + 5.7o+-5.i25+-d.2io 



4r20.i f ao.7+-20.2 8+-20.84+-20.aio 

 +-70. 1+70.P+ 70.4.5 

 +-252.1 

 Corolt 



