SERIERUM SINGULARIUM. 
27 
1 —y 
-! I „-8 (l-r 2OT )(l-r a>W ) ..-3 (l-y- 2m+2 ) (i-r 2 ^) I Ptr 
1 W“ 2 1 (l ?/ -2 ’1 fl W~ 4 'l f* '•' -2 ' (' ^ t* 
y~~) (1—jr*) 
i tum 
(i—y 2 ) (!—y 4 ) (i—y G ) 
•y “ ' v ( 
usque ad terminum un -{-l 
= (1 — y - *) (!+y“ S ) i 1 —y -3 ) ( 1 +y -4 ) • ■ ■ (1 ±y 
P] 
Quodsi hic pro y accipitur radix propria aequationis y n —1 = 0, puta r, atque 
simul statuitur m = n — 1, erit 
i—y 
i—y" 
i—r‘ 
1 — r~ 
1—y~ 
l—y- 
i— y 
1— r* 
1 — r" 
r c etc. 
usque ad 
-y~~ i- 
‘in—2 
1-y- 
ubi notandum, nullum denominatorum 1 — r 
aequatio [7] hancce formam assumit 
1 — r 4 etc. fieri = 0. Hinc 
1 —1— T —I— t 4 —1— ?* 9 —[— etc. -j-A n ’^ 2 = (1—r 4 ) ( 1 —)— v 2 )(1—r 3 ). . . . (1-f-r n + l ) 
Multiplicando in membro secundo huius aequationis terminum primum per ulti 
mum , secundum per penultimum etc., habemus 
(1 — r” 1 ) (1 -}- y~ w+1 ) = r — r~ l 
__ r n-2_ r -n+2 
(1 — r- 3 ) (1 -j- ?*~ ii+3 ) — r 3 —r~ 3 
(1 + r~ 4 )(l — r~ n + 4 ) = r n -~ 4 — r~ n + 4 etc. 
Ex his productis partialibus facile perspicietur conflari productum 
(r — r- 1 ) {r 3 — r~ 3 ) (r 5 —r~ 5 } (r n ~ 4 — r~ n + 4 ) (r n ~ 2 — r~ n + 2 ) 
quod itaque erit 
= 1 -j- r-\-r 4 -\- r 9 -f- etc. -\-r^ n = W 
Haec aequatio identica est cum aequ. [5] in art. 12 e progressione prima derivata, 
ratiociniaque dein reliqua eodem modo adstruentur, ut in artt. 13 et 14. 
4 *