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# Title: Leibniz-Handschriften zur Mathematik LH 35, 3 A 27
# Folio 4v, page id 00068240:0008
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tiagnem 
Aeq. (7)
+ 2
33
t al sus inbis sim a intregra. quia ex duobus mimulus semper par.
uHinc a dussi chriangulares a + al. a quidus anferantur al nuneri natuates decinceps ab mtite
restant quadiata a a a.
aq. (5)
.L Ex aq. 4. fit: Lb- Ne  p ca - da.
Et quoniam L, et N debent esse integri, substimamus pro ipsis eorum valores ultem pro uno
fit X sed ita, ut quosdam arbitarios, At aut saltem pro uno sed ita  ut ex ipsis valorit
quoque appareat integro esse, fiet: nemper pro L, substitmamus: Jsm + str
smb
in +h
4
Aeq(8
in+h m+h tcy.7
m+ B ga fiet neu mn inga +hga ohib
snb - Nc B ga. ponamus sub
in +h
Ae (10)
et Na  Nem + Nch  sb 1.
fiet ex eq. 9, hoc aeg. (12)
 (11
pro priore ponamus l p 49a,
in + 48 H 5. g b. Quo valore ipsius m, 
integris  invento p in aeq.  10 substituto fier. (1) Nc Af(- Nc _9 +N .49a)
a
aaequatione 5. Arrgo cresse aoque siticet psi etium  darc cutorem
A ergo fractio integum faciens ud satis suit composita Muteruus: (Z co - Hb Acob - hb - NC e ga
stone libm
c- m H
fier C  A s Il e _ sb m + m.
b sive expercanda h, et l, fiet. col g4.
 H   VA A D. SL. E. xt. n
jam pona
Restabir. cob - nb +
quaeritr Multilus
1
cole - ga BC
5
sb
A
redi
leob
11 ed
 Lb - Nc +g ega.
17
A -D
ar
m
=1
Restier cbi lib Ccols N
n. le
TNc. Jam pontumus C0p C54 + 98
fit n
1) Nc, ade Explicatok en m fier:
lea
ad
e
1s- gat
a 2  NCd
pone + C. et Le M+d. fier
 Mb a et _ P  ga inde fieri potest:  Mb - Pc   a
Quaeruntur ergo duo integri, ita  uno multiplicato
per numeraem, datum, et alio per alium datum differentia inter productot sit  Unitas.
4
sed quia hoc semper fieri in integris non potest, ergo nec methodus isa succedit
eo casu, quando autem sucredit,
e. g. 3. et 4.
307 H 21.
45 20.
solulum ae problema. Non semper succedere ex eo patet, quin e. g. omnes multipli
denarii teminantur in 0. et omnes multipli quinarii in s alt impossibile est 
diffeore eos unitate. Quam sm b et in genere multiptos ab in si b. et c. sint primi
inter se impossibice est eos differre unitate.  siit 1. et 2 nisi
v.g. multiplum a 3 et mallipum a 6. estae possibile differre unitate
omnes multipli a senario terminaotur in 6
Mb - PC = a. ponc  Cp D c p d - a. et l1
inus exosis sit 1
si sum sit MCcsb. - Pc p 1 ficret 5b - 1  . Ergo sb. non foret
c - 1
integer nisi PC - 1. sit teger 1. seu PCB2. a 70E Or
Quid si 1 sic: Mab - MF Mtc  a. patet M. esse imntile seu B.. Hinc
concluditur tam M quam hoc sensu col debere M esse numeros primos inter seore
mo Lb, et Nc fore primos inter se. id est L. et N uti b. et C.
ponrc
bp bp c + d. tei ME + Md - Pc  a, fict
Dc
M
Haira ataram arareu e
Multiplus dati numeri
MB  PCrahigo M A PC + a. Utque f quantitas fractio esst, tantum quae.
C + d 1
gutur, quomodo ex ipsis  queat compori
Numerum et nt Namerum invenore, qui mullisa  datum, addita unitate dividi possit
per alium datum.
vig.
dividi possit per 7 is et
vel pro E ponento d, fier
b Numerum invenires qui unteliplic abus per 4, et motate 
4+
VPn5,
cp+
b et C +1
cp 2d., et b p 3d + 1. unde 2Pa +1. Unde:
ue qunit
u
a b, cuict
ques mulliplo
a c, unitate
aucto
212 β.