De AEQUAT. ALEBRAICIS 401 



Cum autem aequatio sii 



xs— A'a:'— B'x'— C'x— D=0 , 



expresso nunc soliio symbulo P^ aggregate polentiarumresi- 

 marum radicum, erit ut nolum est 



P, = 2A' 



P3 = 3 B' 



P^ = 2A'J-f-4C 



P5 = 5A'B'-h5D'. 



Hoc posito termini primae divislonis 4A'-l-4B-f-4C'-t-4D' 

 -l-4E^ erunt aequivalentcs 4P,=:20A'B'-k2^D' 

 Termini divisionis secundae reducunlur ad 



_5A'(B-i-Ch-D-hE) 



_5B'(A-i-C-i-D-+-E) 



— 5C'(A-4-B-HD-f.E) 



— 5D<(AH-B-f-C-4-E) 



— 5E'(A-4-B-t-C-HD) 



sed A-*-B-t-C-+-D-f-E =0 ergo 



. _5A<(T5-+-Ch-Dh-E) 



— 5B4(A-HC-f-DH-E) 



— 5C'(AH-B-f-DH-E) ) =5A5^-5B5H-5C5-+.5D5-t-5E5=: 

 _5D<(A-»-B-»-C-4-E) 

 — 5E^(A-f-BH-C-FD) / 

 5P5=25A'B'-+-25D' . 

 Termini divisionis tertiae reducuntur ad 

 — 1 0A^(BVC-H-D2-H.E2) 

 — 10B3(A2-+-CVD2-i-E») 

 • — 10C'(AVB^-hD2-I-E2) 

 — 1 0D3(A2-hB2-hG2_hE=') 

 —1 0E3(A^-t-B'-HG'VD2) 

 sed 



