A"^(9«, 3) — (3n,1)(Gn,2)-f 



De aequat. algebricis 459 



(3 «, 1 ) ( 3 «, 1 ) ( 3 «, 1 ) V 



2.3 



(3«,1)(3n,1)(3^,4) 



lV=:(9n,6) — (3n, 1)(Gw5) + 



-(3n,4))G«,2) 



(3n, 1)(3n, 1 )(3n, 7) 

 C"=(9 «, 9)-(3n, 1 ) (Gn, 8)+^— ^-^'-^^ 1— ^ 



,, .... ,,, (3»,1)(3n,4)(3n,4) 

 _(3n,4)(G.,5)-h ^ ^(c) 



-(3n,7)(Gn,2) 



, (3n, 1) (3/2,1 )(3«,10) 

 D"=(9n,12) — (3«,1)(Gn,11)-f^ ^^ ' m > ; 



2 



-(3«, 4)(Gn, 8) + (3n,1 )(3n, 4)(3n,7) 



,^ ,,,. .. . (3«,4)(3n ,4)(37>,4) 



— (3«, 7)(Gn, 5)4- -^— 



— (3n,10)(Gn,2) 

 etc. etc. etc. 



Aequatlonibus auxlliariis (a), (/»), (t) notae fiunt expressiones 

 (3n, 1), (3«,4) etc. (6«,2), (6«,5)eic. (9«,3 ), (9«,6) 

 etc. ^ ideoque et coefficientes A , B, C , D etc. A'j B', C'^ D', 

 etc. A", B", C", D", etc., sicque determinata erit aequatio gra- 

 diis 12/n.-4-1 radices habens forma aa-{-a''b, scilicet 



12n-t-1 , . . 12in-1 



a^/MN +aVM*N' 



expriinente a quamcumque radicem ( 1 2 n -t- 1 ) esimam u- 

 nitatis . 



Ex hucusque diclis deducitnr aequatioiies de ([iiibus agitur 

 determinari ope aequalionum auxiliarium (a), (b), (c) , etc. et 

 aequationum (a), (6'), (c'), etc. Quod attinet ad piimas evi- 

 dens est lex qua ipsae proccduut, et quisque facile viilct eas 

 esse pro aequationibus gradus 20n-t-'l radices habentibus 

 formae aa-\-a^ b , 



T. V. 



58. 



