207 



illis in infinitum excurrentibus GoniunQim finum et cofinum 

 angali n (p reuera exhibeant. Hae feries geminatae ita fe 

 habent : 



(^yy^^-lZl . (2j)"-3h-(!^.(^) .{^yf-^ -etc. 



£m.n<p-x 



I I. a 



n-4-2 I 0^^-3)0^-4) 



cof.n$=| 



(lyy-^l . (.yf-2^ n(n-:^) ^ (^yf-^-eXc,^ 

 (2yf r(2j)^+2 ,.^ (.j)-^4 



— etc^ 



J. 3. Methodus, qua Eulerus vfus eft in indagandis 

 his feriebLis pro finu et cofinu anguli n (p, fequenti funda- 

 jnento innititur. Polito cof. Cf) n y et cof. n<p-s, erit 



confequenter 



-4^ _ nnl^ ^ fme ^ ^2 (i ^yy) = n n dy^ (i-ss) 



1 s s I yy 



vnde denuo ditTerentiando ;, fumto fcilicet dy conftante, fe- 

 quens oritur aequatio differentiaHs fecundi gradus: 



vnde li haec feries fmgatur 



s — A/^ -f- By^-- -f- C/^-^-j- D /^="6 -}- etc. 

 et ferierum inde pro |^5 rrT^' ^W^' ^^'^^ nafcentium 

 termmi feorfim nihilo aequenturj Itatim ex primo termin© 

 y^ refultat haec conditio: nn — A(X — 1) — 'K- o, quae dupli' 

 G^pi praebet valorem pyq exponente X: fit enim tamX=-f-j2, 

 quaii^ .^5ij-na it^vtprq s duplex emergatfisries^ fcilicet: 



