PROBLEMA ALGEBRAICVM. 123 



omnes plane fa(flores aequationis , x^'^' — i n: o 

 inueniri. Cetcrum obferuandum eft , quod fufficiat 

 vnicum valorem ipfius x eruifle, fi euim hic \alor 

 fit K, rcliqui erunt a, a\ a* ....ci"\ «"'"+"'. 



13. Si in aequatione proxime allata , pro u 

 fubftituatur 2 cof. z mutabitur eadem in hanc : 



■2"(cof. zf- {n- I )2"-Xcof s)"-=+ 1:^:1^--^^ 2^-Xcof ^)'^-'' 



'■ _ (n-.Un-4Hn-s)^n-6(-^.Q;-l.Nn-g^ CtC. I^ O . 



quum itaque fit fin. (/M- 1)-=: 



fin.^( 2 '^(cof.;:;/- («- 1 ) 2 "— Xcof. 2;)"-=+ ll:ii^:ii^ ^«-^(cof.s)"-* 



- Cn-.)(n--_4U«-5) ^n~6 ( ^J^Y. ^ )"-^ + etC ) 

 1.2.3 ' 



fi ponatur [n^i)zzz.^y denotante ^ ferni- 

 periplieriam circuli , cuius radius - i, fiet fin.(;?4-i};5; 

 mfin. 'VT zzo ^ Ynde apparet hanc aequationem : 



2^ ( cof zf-[n- 1 )2"-H cof.;s)"-^ + ^i^;-^f=i^2«"-* 



(cons)"~'-etc.:zio, 



inferuire perficiendae diuifioni anguli. redi , cuius 

 etiam ope notum eft , fadores huius aequationis 



jt'"T+-» — 1 zr o inueftigari. 



14. Hinc vero perducimur ad egregiam transfbr- 

 mationem aequationum noftrarum (G) et (H), fi nimi- 

 rum omncs earum termini fupponantur diuifi per e^ et 

 loco - fubflituatur 2 cof. z , prodibit quidem ex ae- 



quatione (G) : 



2"(cof.;2)"~(«-i) 2«-'(cof 5;)'^-'+^iJ=^--L^2"-Xcof 2)'^-* 



_C n — 3)(n^4)(n — 5) ^n— 6^ ^^^^ ^ xn— 6 . g^^^ 



I. 2. 3 > ' 



