7^ DE SVMMATIONIBVS SERIHRVM 



$. 5. In pr:iccedcnte parngrnpho , articulo fe- 

 euodo, coiifidcraui lub formii gcneral'ori iiequatioi cm 

 I — a .V -+- 3 .V A- — 4 -^^ -H 5 -V* — etc. n: ^ _^^^, pro 

 quocunque numcro x. In quemcunque niinc ccnlum 

 refcratur hacc aequatio , pro calu a' rz 1 , ccrtum ifl 

 legitimo inde moJo deduci poffc valorcs , ab omni 

 dubio liberos ; fcilicet mi.liij licetur ae']uatio per dXy 

 confiderando x tanquam quantitatem var'abilem, po- 

 ftcaque integretur acquatio cum additione dcbitae 

 conftantis : hoc modo peruenitur ad hanc al'am ac- 

 quationcm .v — .v x -+- x* — x* -\- x\— ctc. — -"^— , 

 quae cum nondum clara fit in cafu .v r: i , potcnt 

 \ltcrius dcprimi, fi multiprcetur pcr — ^, qno lc.cfla 

 obtinebitur dx-xdx + xX(/x-x'(ix-\- .vVv-ctc.z:-^ , 

 cuius integralis d.it .v — l.v .v-i- j .i — ^a^ -f-^A- - ctc. 

 zz log, I -f- X. lani vcro ilhi acquario nulti porro 

 controuerfiac fub^tda clt cum fumitur x ~ i : crjio 

 ctiam anteceJcntcs acquatioi cs , cx quibus lcgitimc 

 deducT:a fu:t polkcma , pcculiari fuo iuie \crib eriiat 

 annun.crandae. 



§. 6. In prima noHra ftrie fimplicifllmfl (A) 

 I — I -hi — i-i->— etc. quacuis pcri >dus tx duo- 

 bus faltem terminis conllat , poR quos (erics eadcm 

 relurgit ; confideremus iam (cries pcriodicas trium 

 ter^ninorurn , atque crnPantcr talcs \t fumma tcrmi- 

 Borum pro quauis periodo fit — o, ad quam clas- 

 fcm pcrtinent ferics finuum aut cofinuum , quorum 

 anguli formant pro^riffioiiem arithmcticam. Sit, \erbi 

 gruiia, fcrics infinita (B) i— i + o-f i — i+o-i- 1 — ttc. 



cuiue 



