i86 ATTI 



X = cof. -^ - -!/" ( cof * -^^ - l. ) 



X = cof. TT -*- 1/ ( cof.* -^ T — 1 \ 



«-HI '^ V »-Hl / 



.V = cof. -— TT — 1/ ( cof.** -f- » — I ) 



VI. Pari ratiocinandi modo detnonltrari brcviffime pò- 

 tefl Theorema , quod in Algcbrae elementis (a) oftendit Éu- 

 lerus merhodo a Dan. Bernoullio propofita in Aftis veteri- 

 bus Petropolitanae AcadeinÌ£ tom. III. , niminim aequationis 



infinitae (C) x^ — x "-^ — x ••— * x'* — x — i =i 



radicem unam realetn efTe numerum binarium . Nam ex 

 ProgrefTionuni dodrina fumma terminorum omniunv hujus 



iequationis praeter primum. ed ; propterea aequatio (C) 



degenerat in x°° h = o, feu in x'^'*" — zx^ -»- i = 



X 1. 



a, feu (fafta. divifiòne per x" ) in x — 2 -*- -^ = o,cui 



poflremje sequationi evìdenter fatisfacit pofitio at = 2 . Idem 

 oftendi potell divifa aequatione (C) per x°° , ex quo produ- 



III r - 



citur I --_o: conltat autem ex 



X x^ xi' x°° 



Theorii ProgreflTonum », aflumpto .y =r 2 , terminos pofl: pri- 



1 I I 1 , „ 



mum omnes : " evadere = — i > Se 



confequenter jequationi fieri faris . 



VII. Perpendo nunc aequationem (D) i -+- ix -4- ^x"^ -^ 

 4 AT ' -1- 5 A'+H-^jt-J ..•..■•. "*^ {n-^i)X' zz. y videoque ipfam 

 oriri ex divJdone. unitatis per binqmium quadratoni, (i—x)'». 



ita ut fit ^- =r 1 -+- 2Ar -4- ^x* -+- Ax^ .... -t- (n-^i) 



x" -i- — '■ , ubi a , b per coefficientes Bino- 



. ( i—x )^ _ ^ 



mii determinantur . Fit itaque (E) ùx'-^* ■+■ ax'-^^ — i =0. 



Qua- 



(a) Vid . Leonhird. Fuler vo/Z/fandige tydnUituwg zar tyUgehra . Zvveyt; 

 Theil , Erft. Abichn- Cap.iiJ. $ 2 3p- Vid. etiam verfionem gallicani Jo. Betnoul» 

 li totn.L § 8qo, 



