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# Title: Leibniz-Handschriften zur Mathematik LH 35, 8, 30
# Folio 22v, page id 00068124:0044
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itaque patet fore
p+gh + rhh + 5B + + ht + vh +WH = m divisibilem per b + ch + dhh + et = n
p+ q(les + Xssit) +5 si 3 + th) Y + VB) S + W le - hn) divisibilem per b + clhi) + dlib) relis3 = (n)
etq(tit r suti) + s () F +(tt + v (t. F w (td - (sin) . . . . . . b + esti) t dssuistessu-
sed nsunt
sunt ergo n divisores respondentiam m; et insunt dati quae siti inter plures
datos. Praterea b est unus ex divisoribus ipsius p, et e unus ex divisoribus ipsius
W, si n et e sint termini summi. Itaq verus divisor ipsius in, qui sit n quaesitus, si divida-
tur perh respondentem, quotiente iterum diviso, et quotientis quotiente, quamdiu li-
cet; dabit residuos primum b, secundum c, tertium d, ultimum e, posito
omnes literas esse affirmativas, et h divisorem esse majorem, quam b vel c vel d
etc. Nam eh3 + dhh + ch +b = chh + dh +c + et ehh + dh + c = eh + d +
et en + d = e + a et e=e ubi b, cid e sunt residui, si sint minores quam
n
k
h. Veri autem divisores erunt, qui ex pluribus hypothesibus h vel (h) vel ()
semper residuos dabunt eosdem, ad eoque et hi residui b, C, d, e, veri erunt et ha-
bebuntur: adeoque habebitur et b + Cx +dxx + ex dividens formula, qua
desiderabatur.
Ex iisdem patet et alia Methodus, ubi nil refert, quae sint signa coeffici-
entium, et quae sit magnitudo ipsorum h: modo h assumantur progressionis
(n), (2) et et
Arithmeticae, velut - 2, - 1, 0 +1, +2. Ita enim ipsi veri erunt, qui combinati
dantseriem, cujus differentiae prime, secundae, tertiae etc (prout dividens formula
quae sita est primi, secundi, tertii etc. gradus) ex hibebunt quaesitas b, ci d, e, etc
Sed ita combinationes plurimae, et tentationes imutiles instituendae erunt
quas nostra methodus abscindit: et eadem opera divisores formule cu-
juscunque gradus defimuntur, re omni reducta ad divisores mumerorum