De AEQUAT. Al.GEBnAlCARL-.M ETC. 73 



Taiidcm invenlemus 



B'' =:«' r' 4- 5 a' /•'> 5 ^-10 a' /•' .v' ^-10 «' r' i' -f. 5 a' r *■* -i_a'° *' 

 C ^ = b' r- 4- 5 // /•* * + 1 i V *• + 1 i" r' i' -t- 5 h' r s" ^b'" s' 

 l)'' = cV'-|-5c'r''i + 10 c'r'i'4.10 cV j'-|-5 cVi'*+c"> j' 

 !•;'* =:</^ r' + 5 J' /■'• * 4- 1 (/' ,' i' 4- 1 (/' /■' s' 4. 5f/^ r *'* -J- d" j'; 



ergo 



r, = (1 4.«^4-Z<^4-c'-}-(r)r' = 5/'' + 5i' 



4_ 5(1 +rt'4-i'^4-c'^4-rf')/'*5 

 »^10(1 4-a'_}-i'4-c'4-^/')r'i' 

 4-10(l4-a'4.i"'4-c"'_f-^=)r'^' 

 + 5 ( 1 4- rt' 4- i' 4- c' 4- </9 ) r J* 

 4_ (1 4-rt'°4-i">4.c"'4-r/">)5* 



Seel ut nouim estP,= — 2A = 0,P, = — 3B,P^= — 4C, 

 Pi= — 5D ergo 



atque si loco B ponatur 5 B", et loco C , 5 C, B = — r s' 

 C = — r'5, D=— r*— i'. ' 



Ex duabus prioribus deducemus 



s C s B' 



idcoque 



T^ , - C' B' 



Acquationes igitur quinti gradus cujus radices sunt formae 

 ar-\-a^$ resolvibiles sunt. Earum forma generalis est 



C B' 



cjnsque radices 



a:'— 5Bx'— 5 Cx — -— — =0 

 B C 



T. T. 10. 



