NACHLASS. 
THEOEI A INTERPOLATIONIS 
METHODO NOTA TRACTATA. 
i. 
Problema. Invenire summam seriei 
a n . b”_ 
(a — b){a— c){a — d){a — e) . . . ""l (b — a) (b — c) (5—d){b — e) . . . 
_l * I d l 
^ (c — a) (c—b) (c—d) (c— e) . . . ' (d—a) (d— b){d — c){d — e) . . . 
e” 
[e — a) (e — b) (e— c) {e — d). . . ~ 
ubi a. b, c, d, e sunt m quantitates diversae, atque n numerus integer quicunque 
positivus, negativus sive etiam 0. 
Solutio. Faciendo brevitatis caussa 
(a — b)(a — c){a— iZ)(a —e) .. . 
1 
{b — a){b — c){b — d) (b — e) . . . 
1 
(c — a) (c — b) (c — d ) (c — e) . . . 
I 
(d— a) (d — b) (d- c) (d—~e)T. . 
a 
€ 
T 
S, etc. 
ita ut summa quaesita, quam per S n denotabimus fiat — aa n -{-'Sb n -\-'yc n -\-$d n -\-etc.: 
manifestum est, si ac exprimat quantitatem indeterminatam, ex evolutione ag 
gregati 
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