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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 1
# Folio 36r, page id 00068196:0071
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Merhodus ed pro investigandis divisoribus aequationu
e
dgregia, ut idem problema quaeramus diversa via. sen obtinea
musque pro eadem incognita diversas aequationes. aertim quarum
haet est
leinde divisor communis dabit desideratum.
s
si aequatio divisibilis est per aliam rationalem utique sed terminus ultimus
amu
ratio nalis.
aa
dioisibilis
4
ret A +2X + 1x - 18XX
X + 2XX + 1X = 1B = 0 nulti plicetur per XX + 2X + 3
+ 2X + 4X + 2XX - 36X
+3X +6XX + 3X
X+4X + 8 X = I0XX = 33X =54
a
i aequatio sit divisibitis per X
Pro es substituatur V + 1
ponamus aequationem secundum X
potuisse dividi per X+b, erit
aequatio secundum y divisibilis per ytbr
is
ergo comparando duos divisores inter se, aequationis nem ultimi scilices
x et in aeg. seludum, ii demum valebunt, posito
n
termini in aequ. sec
dividi posse per simplicem aquationem, qui differunt unitate
nis
nonamus aequationem drodi posseper. Xx + bx + c et fiat X = y + 1
aequatio dividens
erit ausor
s
y +29+1 Ergo eliu sunt cro otorjores
+ by + D
si divisoo procedit
er adeoque divisor novus secundi termini erit b+et
ergo fiat ad huc Y = 7- 1, et prodibit 3t - 27 +1 pro nova aequatione dividente, ergo divisor
praecedens
divisor ultrmi termini erat c + b +C ergo
e
et 4+ bg b
C
iatum termini est 1 - b + c, et paror erat est
2 +2c quorum dimidium cddermo 
eligendus divisor primi ullimis terminis, C Qui a Rmidia divisorum summa a duobus reliquis summa
summa duorum divisorum ultimi, termini est
CX
distert unitate, ad invenientum uttum aequatio proposita sit divisboris per 49. 2d gradus
porro invento e, habetur et b, cum decur 1b+C=