# Leibniz Legible — https://leibnizlegible.com
# Piece: https://leibnizlegible.com/api/records/11975/text
# Catalogue record: 11975 — [Aufz. zur Dyadik]
# Incipit: Si numerus per numerum multiplicetur
# Date: 1694
# Akademie-Ausgabe: AA VII (assigned, not yet published)
# Record in the Leibniz-Katalog: https://leibniz-katalog.bbaw.de/de/extended-search?id=11975&katnr=39210
# Work: https://leibnizlegible.com/work/00068255
# Title: Leibniz-Handschriften zur Mathematik LH 35, 3 B 5
# Folios: Bl. 99–100 (from the shelfmark LH 35, 3 B 5 Bl. 99-100 (=39211)): 4 pages, canvases 197–200, page ids 00068255:0197 to 00068255:0200
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=00068255&page=197
# Lines: 501 recognised on 3 of 4 pages, mean confidence 0.65
# Catalogue: Leibniz-Katalog / Arbeitskatalog der Leibniz-Edition (https://leibniz-katalog.bbaw.de/), ed. Arbeitsstelle Potsdam I der Berlin-Brandenburgischen Akademie der Wissenschaften, CC BY 4.0.
# Machine transcription. Not an edition. Errors are expected: about 8% character error rate on Latin and French lines, higher on German.
# Licence: CC BY 4.0, Leibniz Legible. Machine output: do not ingest it as verified text; keep this provenance with the text.
# Wording rule: say "the machine reads it as …", never "Leibniz wrote".
# After the first blank line, page by page: a "## Folio <label> — <page id>" line ("## Canvas <n>" where no folio label is recorded), "# " lines naming its source image and model, then its recognised lines in reading order, one per line.

## Folio 99r — 00068255:0197
# Source image: https://digitale-sammlungen.gwlb.de/content/00068255/jpgs/default/00000197.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 193 lines, status machine
1c
F3 F _
Et CF  E
1c
C E
E
222
rt
pr
6 
45
 s na Riasis
 =B 13 X Ee Bin 15 B. .
33
6 Er
e
p
isseu
isuensi
go n vae
ducibr vuussguo viram)
ogrig munq cunubo
quiupp. mnnz usuei anpdoif
gruxp. SId m. 5o est B 17 seit 127 V
bo
mequ0g quo ne quaragut
eno
L
ou nos oyb vole G.
utcalque nococheg oesse
iolua
si numerus per, numerum mustiplicetur in prmus quidem sede sit oifu) Ergo
si en prossundit vel odelovelo vel 1. id est o, cum paroter par p in parter parer parte par in
parter imparem par in parem, par in imparem; cinpar in parem; id totum cum
impar in imparem. In ecunda sede sit 000 sunt 16 casus, et prodit D in buo dicim prioribus
seu in 4. = 4; Nempe cum pariter p impar vel par impariter impar in dpanter
imparem vel impariter parem ducuntur, nam in altermationibus multiplicantur numeri 
casuum in prducto ex comhinade Fiugenda jam essent Nomina pro terva sede, me
Fritque numerus in secanda sede obi primo sede erant numerus par impar. Ob secundam es
pauter
par pauter impar, impariter par, impaniter impar. Ob tertiam edem est nulmerus
parit pariptariter imp par. Jari pariter impar. parimparise sa parim parter impar C.
pr imparisariter par imparipariter impar.
par 0
inpar 1
pariter par 00 paripartter par 6000
upar
impar 01
impariter par 10
 unpar 1
Porro patet hons
parimpariter par
impar
imparipariter par
impar
imparimpariter par
unitatem semper esse
in multiplicando, unitalem mparimmonteria
pro pro producto semper rariqon
contingere, et fpe quanum 9s -b16
in pumm sedes sede un
parfecasicum productorum;
X
Arq
etB. C
a ac 2+ (2) in 24 (2)
a + (a) in a + (a) dat aa + 2 a(a) + (2) () 
ubi aa sunt 0, et 2a a) sunt 0, et
par
solum (a) (4) dat 1. si autem a, et (a) 2.1
sunt aequales, ut hic patet (ati) fore
partem quartam producti ex a + (a)
8.0
eso
1E0
881
proprietates poterunt inver
sul et apparent an
postibile sit
 numerum
alum
productum Numer
per Numerum
sic
O 211
2.D.
t e
111
e
a son
de
Sic impari parimpariter impoli foret 1011.
Hini porro si ingenerali considera nt.  ibo 
in a + ()
tone producti numeri per nuculum 9.5.0
igar
i
et 113. 1 st 10I
Hinciam ac
et romene la
fura patet
et modu
nexprimendi e
quemlibet
sine veri
quia in altioribus
sunt paulo
perplexiora
-0
 imparipariter par impar foret
00 1
010
011
100
101
110
107 8005
1.1 - ∞ - ft. a F10- BVd -
21 _V 85. 1 9161. 22H1.1
20 +ED 85.0 96. 0 2tL 1. 0
2)) t1.1 8. 14 911. 
1 10 - 210- bro - 81 d 8i1
(t d+ c + b ta
810
10-
2.1 b5) 85. 1 510
bo 210 10 810
ete
et e+ C+ b + a
et
q es en et
1.0
sora
al = 67 0. 1 in (0) (1) = 0. 0360, 1
am = 0011lie 0) (1H = or 04 vel 0g, 14 = bl
b1
d an = 3c0)  ) sed excogilandae ad hec
Hic prodeunt alterna et
tivi alterntivom
alia rationes in
ut distinguantur commode
aam, et bl,
jutigi
sufficeret forte pauciores
esignari, ubi prodit i
Heliquos exceptioc
meelligo
pares eu productos per 10
ves
et ila p0
fio
 di pro ducto seu non
Dc
b
t E.t B. 5. 1 geti vsitt. 1
1o vio 4VO Beo gero
1.9.
11 - 0 - cb- vo- 80- dip- quorramus coma
Alia est consideratio si consideremus ses
ilia 8li.4
seu productos per
nun qvo
1. 1
10 20 40 8990
bI 21  81 9l. 1
11
15.
1020- 40- 40- 910
bet LEI e4 des,
I uo eo 
V 1
eo 20 sb b dF
1b ve bb gC 4b a+b-
9t
600000001111 1111
0o leropurer ont
ect
1. ()
vit
101
tand
ittic semper prode
simpliles
soli alternativ
Hic opus addiliome alternatioom
eu
simoes
marios
ut regula
100 1 10
a + b = 010101
let B = 010101010VOT = 0100 101
000 , ii11

## Folio 99v — 00068255:0198
# Scan: The same scan is also registered as fol. 100r; its text is given once, here.
# Source image: https://digitale-sammlungen.gwlb.de/content/00068255/jpgs/default/00000198.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 124 lines, status machine
o omno
orter 01
ion
101
300101
0000 0000 000000I
0011, 01
10001
d
ton60B ooVOI
10c0111, 01
100000101
0000
20do mm 3d 160 0 00VOIII
0
obum 0000 1010
1100, 01
ioor
30d0 10
01 per 01 = 01 01 per 0212 = 0291
orper 04 p4 = 04 o12 01 per 0818 = 08014
O2I2 per 0912 = 02n _ Et our pr 041 -040
O2 12 per 0518 = 08 oruZ o12∞G F6) -0() orn
1B0C per A x 
Hino oere pero
eest. 2, 4
8 1b
in 1 m n P
quan
Huat
nducca
(n est 1 2 4 8 16, eu dus c 
om, oere me on
1e ∞H c
eguus eq oypr
al= _ e (401 al = 09, 01 = 0i
bl = oor 0212, 01, = 02, 01. 1 am = (1) o(2)0o2, oi, 1 btam-2140
c = 0414, 01, = 0o12
an = 2, o12 bn =  02122  motues oetroter (
dl = 0818, 01, = 08, 0 4 ap = 08014 31 = 08014 bn = 0+ o22 2
video generaliter simi quae sant similis compositinens
semper pro unico transferri posse
itaque se fiet
dc ba
d 4 bus du ae o at
ex in n
sequentem
ig
0  8
a o
ised
32
 uis moreu qui abets in r eti per etres pri
al vinarus. omnis numerq
sis genull, nec qui
Generatem torminaturm per a est primitivus
111 1 1  ecc. divido per numtrum imparem
seneralem diadice dispunctive expressum
nemper per E 42 41
octe 0g.B e8. Brt 
s
0 per 8
OP. β per ox.  = d1 v B. 
si
oβ. B in oB. B = 06.6)
3 et X pares
1B0(B per 6) = dA 1B0B 2
posito st pB
ngrssim
E sempiget
iveet aqualiter sor
e et M lsistum oere de e oeie
e sime
si e major ent oere per din 
et oiem per om erit ore
V our
Ergo oece per omem erit om
Eai cae) 9 016 ). l66)
0
5.
cum dicitur exc
entelligitur  et 15. 0
et isty esse d
et 23my esse 0
orudit met e
Hota 0 vl punctata nota
n
aussil
tem
e i
5
e
2
20) 30) 2) 2
 m sid +
peotion
h
+a
m
ption
fict
unadiam +bn
am=  0201
12. hyuamibm ori
Ergo om bmorio
an 012
it 16 8
n 16
2+ 
6o
 
x. Ex exo. ct
exc ex
150 10 1310
u oa
3-1
3
e
emplicantur
Mero ved
1.1 aequ  s et p
 merse excuo
ca.go, c
ercorm

## Folio 100r — 00068255:0199
# The same scan as fol. 99v (00068255:0198), where its text is given.

## Folio 100v — 00068255:0200
# Source image: https://digitale-sammlungen.gwlb.de/content/00068255/jpgs/default/00000200.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 184 lines, status machine
 p
Cd  C)
8d
e sd
e
23
34. 8
et. 8 a-
1. 12
2A. 
is
5f3
set X
is 00to re101 cu 106 o0 fo14010
1066000
15E L
23
dsc. 2 ∞73
esst f 3
3353
E5+E
5- 1e1 5 p.e
50t5b8o
et
22
541
8, d8.
160500d01 602
ex ens
2d
e
e es inter
030
e cm
= 223
eei
D ( 519 3  +
5
e (5393
sa
 Haec divisio dilcyentim instituatis
5∞
1∞ 223F ud 2
5:H
1
ess.
61
festunnda fu
10 E
SesElEl stit:
1e 5
F., 5 + 23. 22
b 13
lassi
u 
5
3. F. 12850
d 9e. 3
x +
00
-5
5 a 5eit
22-
d8o
68 ss
1.3FC 5 20
su Zc de
1839
2d
2
d3
66000000150
14
5 0- 5
122
s. 2
(+ 2 de a
e
sC
0523
ui 
c
123
u unieL 3
 ad
e
6= d
s
Nec oretur commovissima
ratio sic diritendi incipi
it die 18 9+ 92 2+ 1
1F11
Forte lamentiabil ad hunc
 eit 28 24 22 2a 1
1in -.
ost ob b at b by
031 ops -08 - 0 + - 0. 2 -0: 1.
cstriie bi osse bt
8 R 5. 0 -7
fine et diufere 10000, er i  3. 40
more solilo, sad tunc
numerice
1
107 3 1 12p
207 3) 5  ac aud
2  S 8. d 15140
125 t vd
it p. 
at J. 1)8
si  8Is 
i
1t 0
und 2 3+ 2gto
a 11 2_
1 1
vE (132 exopud- 3gt B, 9) 1 31 a7A1 55est.
sien a e b
Eosq risseb
7) oyc
ILeto 2gest, L est 1 61 est0
e Sresto apst 5t0
exent quod 1. 23HO AiBo Fpi Sc gevo mesto
sisie
areat
cudiab. Tandem
oportet cglingers ut
residum aequem tandem
crvisori, X ibi finis
per gram eundem,
ende duam pnde qeu
ulsiguoC
et
i
Lc
 (
14 3
1d
2 =5
55
dd
3.0 )
 E f--∞0--
8250 su0 0-0b--
52
o
(5D 0v (000=5- 5--
2-
25t.
E
=d 
C8
0= 3
2-0
 5
)
nats
F8
83
20
Se
5 b 3ei
11 11 ∞0-
∞F.
eu
i e
in- lu-
-
dude
10
 i
2t 173 205
 =
Et
22
E S
+5
e
49, 51, 53, 155 1 9.  3 F F
Egeto itst p  109 est
(detahenda adhnc 49 4916a, 51, 51tSq, erc. ut 8
tandem de quod est exceptum Ries accuratius potem
eassmi, in appareat, quis gru quod quomo quae
precpessio collendonui insequent et quae exceptorum progo
partim et asterisco in ipsai serre se regut