520 U EULERI OPERA POSTHLMA. 



Varia. 



(quoniam ad hoc binomiutn 



2/- 1 



reducitur, existente n numero infinito, atque hujusmodi bjnomiorum omnes divisores assignari possunt), esse 

 productum ex his factoribus 



i->iiolgi4|-^ Wi-^i-^) (i-^) (1-9^) (i-i^y^e»c; muUiimtihmim 



unde in genere hujus serie^ j o^j Xm idvtom^.iH .^7({f| jo .iTi'Vd)H«i nombnoq^^nWJ: 



^ ' * OM "• ofn ""^ ,//} "1 ' eiC. 



.803niJno#'V^Rtib9fll ODpzooufl yr VrijT ^* oq ,?.ri'!)JiI i*i »Iua .Ifl «ui^qi ef.hr.. 

 summa, si m fuerit numerus par, exhiberi potest. Tamen huic methodo aliam magis genuinam, a me nuper 

 detectam, praefero, quam sublimi jndicio Tuo, Vir Amplissime, omni observantia submitto. , 



- iJiia^sivi p^ solitas integrationis regulas inle^rale hoc .,, 



/xP irfa? 



idque partim a logarithmis partim a quadratura circuli ita pendere deprehendi, ut si addatur 

 .loluH gabTBiifloai .0 .*! .d iW -^^p—i^^ imA 9«fpi6 o«iia?,iJlu8f! 



in mtegrah summae partes a logarithmis pendentes se mutuo d^struant, eae vero, quae quadraluram circuli 



■;■';;:-,: ■, ■",. '' . T-- ■' r.' '.'..,' . , 1' i • f -1 ■ ■ •■ •• ■ *'*''' '■''*''!> rf>,fA-,-;:f; (!,.■: ■ .: ■) ').!ti,-i;.t< 

 ppstulant, duphcentur. Investigavi igitur mtegrale hujus lormulae 



^ ' .<;;■; ha^rfisibm. RHajb ft'jtfl^ji»4JsfO (;lfl»yni aupitwaiiii 



rxP—i-^-x9—p—i , ' . / 



-f)ri9y ,9joqu»ajs s. ueJo-iipiq Oitiiamvj - — — j-Z. — 7 ^ '*^® ,nifiJid!»D moaoiios mfiisitftiig 



ita sumtum, ut evanescat posito a?='0; quo facto, posui x=.\, atque inveni integrale hoc casu ad hunc valorera 



,"iiyiauo'.ij oiiJf.oa iijiijlioxa /iuu bs JiiJyq a£i'iu3i.bii0iuun)a .•;£» 



- ,!,-.i ■: - ■ ^■■^vri ^ ^=i -■ '', ■ ■ ^ ■<■' *■;■ ' 



-moDiftiwa faujfl£up tobnsaifiioa laula&i ■"•■■ •''•- " ■■ '^> ■•■ / ■ > . .;n", iM- liuj 



.,:-■- >;-f 4- V^ '"f n.«a'Vff.:j^;Hnf.' ^'1 o sin ^ — , r •• r ' 



^ g '!«ii( «r;'ilf;-/ Dii.i). >■,;!* 



reduci, ubi 7V denotat circumferentiam circuli cujus rodrus =1, ih quo eodem circulo sinum arcus — accipi 

 oportet. Simili modo demonstravi integrale hujus formae ,n<fii'i9dqi!oq ba iiJouiBib monoiJnj r:I .o;ii;;Juiiob 

 i=i (Blciiidis Jaa i-jBoDilqoiiS mumi-iiilq aurjr, ^^ — i—xf — ^iiilt*!''"^ fiacJiloqoiJs^l fiiju^bsdA B^tiavinii meiJd bsi. 

 .-ojIJbM ^i«itcID 8u[tio jfeanal bucd oigofi mvJ i -^ x9 jl' )*|;i;?i Wi : iijJoioioani rnuuT fitn^-.Aibsdoa biiin 



ebdem casu; quo post integrationera ponitur sc=i, abire in ai<|]rj n; 



i.iaiiai idiiiv-uteapo.; «iudi'ia.ii,-ib ,.-j yiip;. pTC '. ■iiHti lui; 



■.!.;,:•■.,# .:•:■■ . ■^"^i'.. --.■■•• ■,,. TT COS ^ — . • ■' • '. 



fil82%3 BbaUllA ajBjilSy «niO minf.Iu nj;, ;.,!i:.nit-. ::i)__ 9^, jji.i i:jilicj innoi-n .1, 



n -. :' ' •' ■ ftniirin if a.njn! v.r.joit.iinvif, ifM.?'» !v<q s\n A~ '! '''■;* o^v.inl ini>.:i/. fton 



Quodsi ergo illae formulae per series inlegrentur, atque tum ponatur ix=:i, prodibunt duarum harum seri- 

 erum sumraae: 



(iilnb , nioiojaon^o') i auiaqi tmibert ^hiiiaQtii iie>h3im'\ nnia sunKnio 

 ^ , _ 1 ,1 r_; 1 1 ^ 1_ ( 



J»1U13/ j .P^r p q-p q^p ^q-p ^q-t-p-^Sq-p 3? H-p *^ 4g - p *** 



xnui!i«04 i>li.'i'.',nujS!Lib iiiijbiup oiUia liioJiJi; iiiijjij.aii;: aua OioJuiUfij aJfiJiio/ iiujo ■jLhirfM 'jin. 



n cos A — 



1111 1 1 1 1 ■ 



*- t: ; 1- elc. 



'«V iLwwSv o »in ^ — ^ ^~P *"*~^ 2?~p ^q-t-p Sq — p iq-t-p 4q ^ p 



