De AEQVAT. TRINOMIALIBUS ETC. 335 



2ab—fb—1=0 

 2ac-{-b^—pc=a 

 2ad-h2bc—f?cl=d(i 

 2ae-i-2bd-i-c2—pe=:Q 



2ah-h2bg-i-2c/-^2dc-^/i=Q 

 2ak^2bk-i-2cg^2clf-i-e ^^pk=0 

 elc. etc. etc. 



Ex prima harum aequalionum deducilur a = 0, (i-=p-^ sum- 

 pto a^=0 , ex aliis aequationibus habemus 



i —1 d=^- —~ f— - — ;— ''^^ 

 p' p^' p^ p"^ p^' p^^' p^^ 



Erit igilur 



_ q q"^ 2q^ Sq'^ \4q^ 42q^ 'iZ2q'^ 

 p p^ p^ p'^ p^ pii ya'^ 



quae est series superius inventa pro valore secundo incognitae x. 

 Suniplo autem a = p iaveniemus 



_ 1 _ _1_ 2_ _ _5 14 _ 42 ,_1_32 



"""d ' p^' p^' p"^' p'^ P^^' P^^ 



ideoqne 



q q^ 2q^ Sq"" 14q^ 42q^ 132^7 



a-==p-+-^— — ,H '- '- -< 5- n-H -f —etc. 



^ p p^ p^ p' p^ p" p^^ 



quae est scries superius inventa pro valore primo ejusdem in- 

 cognitae X . 



Examini subijeiendo coefficientes numericos harum serierum, 

 nempe 2,5,14,42, 132 etc. reducuntur ipsi ad expressiones 

 sequent es 



4 5.G G.7.8 7.8.9.10 8.9.10.11 .12 



2'2.3'2.3.4' 2.3.4.5 ' 2.3.4.5.G 



etc. 



Erit igitur 



T. VII. 44. 



