De aeqlat. algebhicis 



455 



(2rt + 5)^2« + 3P2/;4-5 (2«-f-3)^2;t4.3^2«-<-5 



(2«-j-3)(2«-i-5) (4m+8) (2«-i-3)(2«4-5)(4n.f8 

 =(4n,8)-(2n, 1)(2/i, 7)-(2«,3)(2,;, 5) 

 Scil icet 



A' = (4«,2)J-^Ml(iZ!:l)\ 



B'=(4m,4)-(2h,1)(2h, 3) 



C' = (4«,C)— (2n, 1)(2«, 5) 



(2«,3)(2«,3) 



(*') 



D'=(4^,8)-(2,/,1)(2«,7) 



-(2«,3)(27i,5) 



Quantitates (2/2,1), (2 «, 3 ) , ( 2 n, 5 ) etc. ( 4 «, 2 ), (4», 4), 

 ( 4 n, 6 ) etc. uotae Hunt ex aequationibus auxiliariis (a) , (b) , 

 ergo et noli coefficicntcs A, B, C,D etc. A ,B',C',D' etc. atque 

 ita deterininata erit acquatio (jnaesita, sen forma generalis ae- 

 quaiionuin gradus 67i-4-1 cujus radices sint aa-i-a'b, sen 



Gii-(-< ^ 6n-«-1 



at/ MN" -+-a'|/M'N% exprimente a quamcumque ladiccin 

 ( 6 M -4- 1 ) esimam unitatis. 



Eumdetu calculiini instituendo pro aequationibus gradus 

 12r?-t-1, quaruui radices sint formae aa-i-a''b, invenicmus 





imde aequationes auxiliares 



(3«, 1) = (12« + 1)MN 



( 3 72 - 



(3«, 4) = (12n-}.iy- 



' 3 ) . . . 3 u 



2.. 



MN' 



(3«,7) = (12«4-1) 



(3re,10) = (12ra4-1) 



etc. 



(3;t-t-G)...(3/i — 1) 

 2...9 



(3n + 9) ...(3n — 2) 



MN' 



2. ..13 



m:s^ 



etc. 



etc. 



(12n,1) = MN'''"*"+M^N' 



(«) 



