Opuscula. 
Invenio 
A(m).i^A{m)5-- " Tx ^ di:^ 
'ACm)»i^Aim'),i*^ i — ^ + 0 ^ _l ^ 
"~ d x°-"''' 
Af -X At 's ^ d.A(m''^i).i.^2 
&c. 
Et generaliter A(m^')Cm^\):=.A(m)(m~i)^(m — i) — 
J) fm-2) <^(>«-2) d^ /^(w"-4-2)(w-2) <^ ( v/~z) 
' ■ — -j- ■ — 
d X d x^ 
^ d"-""'. A(rt)^ .Mm^i) 
Numeri & pofTunt efle quicumque, dumrnodo ta» 
men nunquam alTumatur m — 1>«2'*, 
Numerus terminorum hujufce feriei eft = »— ^"-f-i; rai 
nimus /552 -f-i valor tii —zj ergo maximus m erit m' — n—i 
Fingo 
^(i«*"-i-i)(w- 2)a^(w— 2) , 
d^. A (m''-\-i) (m—i)$ (m -1) ^ d"-'"". A(tt)S' ^( m—i) 
" Tx^ ' Ix"-"''' » 
cujus numerus terminorum eft =n — m\ 
12. Ergo fubftituendo in hac formula w^-f i , 
&c pro m" , numerus terminorum erit n—m' - 1 yn—m - 2 , & c 
13. Quapropter valor A (m) (m—i) exk A (m) (m~ 1)- 
A (m j (m—i) 6(m—2) S(m~-^): ergo ponendo m= 3 , 4 > 5 
&ci&in ^ (;«"). 2 , ^f«/ >3 , &c fubftituendo valores y^f>«^,x 
Ji(mJ,2y &c; habebitur A (m)(tn—i) — A(m^ )6,.S(m—2)'- 
d^i.. o(«g— 2) — \-ci„o(m-2) '■ " , - — - — f 
:t a^i...^ (m- 1) 4- ^ 2..^ (m -2) i^+o^^..^ (m-i) S 
in 
