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# Title: Leibniz-Handschriften zur Mathematik LH 35, 4, 17
# Folio 8v, page id 00068014:0016
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si numerus propositus sit impar. Sumatur
ejus duplus. 2Z.
a
14Y 2 _B aequ 1 + 2Z + + 27. 9-1. 
1
et 2Z- 2 aequ divisib. per Z. Si Z sit primitivus.
2Z. 27, 1. 27-2
1. 2.3
Hinc a + c + eequ aequ. b + d+ f etc nec coincidunt
ut in impare. ecu
a+ c+e ecc - 1 (est divisibilis per Z. si Z est primitivus potet
seu b+d + fet-v,
Cb7 d + f erc = 1 est etiam divisib. per Z. patet etiam ex
ex terminis
terminis posito Z esse primitivum
Unde e0 casu sunt condioisibiles si y non est primitivus
2, 2 aequ. f + Z0 2- 1 + Z. Z- 1. 7-2
i
1.2.
1. 2.3
et (. + Zete
Si jam Z non est premitivus, quaeritur an possit esse
ponatur ita
esse, et sit 2 - 2 divisib. per g. erit etiam 2- 2 - Z
1. 2
1. 2. 3
etc. 
1.2.3
P
Z. 1. Z-2. 2.3 Ck.
1. 2. 3.4
2
D
1. 2. 3.
Auferatur prior a posteriore, fiet:
etiam integer
1. y - 1
Ergo
1. 2
q- 1
2
+ 2, 3- 1. Z-2
1. 2.3
Z - 1. 7-2
123
+
si Z- 1 est par seu si Z impar erit
e Z.t di 8 divisibilis per Z
ergo 2
2 - 1, Z + 22-20 Z, =C
seu 7- 2 +2 Z. 2. 9.3 erc. erit in leger
se 28 a d anferatur restabit integer
L
et
q integer
MEC
nl1111
Dec 1111IF 111
t
1 etc +I
1. etch.
3. 2- 1.Z- 2.Z3 integer
1. 2. 3. 4
Z. 1. Z. 2. Z-3 integer
1.294
7-1etc.
Z- 1. exc. 7- h
Dy - 1 + Z- 1. 7 - 2 + Z- 1. Z- 2. Z.3 etc +
ert integer.
Jam 2
a
divisio ergo omnibus per Z. euit quotitus
integer, ac proinde
7-1 + Z- 1. Z-2  +
112
etne
posito D aequ. Z 2. Ergo si Z primitivus erit 2. 2 primitivus
ac proinde et q -1 primitivis.
92 esse divisibilis per Z.
y. 3-
divisib. per Z. sive L  +
erit
a
+
. 2.
111
250
2
14 d
Onnus Numerus progessionis
duplae unitate minutae
2 - 1 est integer
si z est primitivus.
Omnis Numerus aliquem
numerum prodhessionis
Geometriet duplae unitate
minutum, dividit
ratio patet ex periodis
Ls cuet
factionum oluior sur
duo dantur numeri enidem
numerum progressionis
ss cometisco duplae divi
dentes, seu qdivisores
com sive confactores potrs
1046
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7b
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300
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Axil 308f28
18761 ccil
16
5
si numerus in progre propressoone trimali binos numeror
UII crc exaste dividit necessus est duos illos
esse periodicos ut si exacte dividet III etiam exarte
dividet 1III. item 1IIaHI. et ita ponomonasos
et generalitur sinumer quod inprimis utele a vimali
proressione.
in Brimali gcessione
111 1 1 11 1
1011
0
11
1
lloci
le
11
2501
1. 3 3 
s
+
22
69
128
1Y L 35 217c
1 ∞ 10 10 5 1
2 6 1520 156
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pot
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ti
p
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100000001
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∞
ees
agu aeq
aequ = + 6 +5 e
u