# Leibniz Legible — https://leibnizlegible.com
# Piece: https://leibnizlegible.com/api/records/11178/text
# Catalogue record: 11178 — [Aufz. zur Dyadik]
# Incipit: Columna prima secunda, tertia, qvarta etc.
# Date: 1711
# Akademie-Ausgabe: AA VII (assigned, not yet published)
# Other printings: (engl. Übers.) L. Strickland, H. Lewis: Leibniz on Binary, Cambridge (MA) 2022, S. 150-156
# Record in the Leibniz-Katalog: https://leibniz-katalog.bbaw.de/de/extended-search?id=11178&katnr=39157
# Work: https://leibnizlegible.com/work/00068255
# Title: Leibniz-Handschriften zur Mathematik LH 35, 3 B 5
# Folios: Bl. 25–26 (from the shelfmark LH 35, 3 B 5 Bl. 25-26): 4 pages, canvases 49–52, page ids 00068255:0049 to 00068255:0052
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=00068255&page=49
# Lines: 232 recognised on 4 of 4 pages, mean confidence 0.73
# 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 25r — 00068255:0049
# Scan: One image of two folio pages side by side, registered by the library under both labels (also fol. 26v); this page is its right half.
# Source image: https://digitale-sammlungen.gwlb.de/content/00068255/jpgs/default/00000049.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 58 lines, status machine
secunda, tertia quarta ete
Columina prima (potentiae naturalium cujusque
nadice ex pressa, habet periodum notarum 2, 4
8l 16, etc.
Hinc nosci potest ex potenta
numerorum o,1, B; vel o, 1, 2, 3; vel numerorum 0, 1,2, 3, , S,
99. vel numerorum 0, 1, 23.... 16. etc. Itaque
iidem numeri inde ab O sumti serviunt pro poten–
tia quacunqo eadem columna potentiae iujiscunque.
0 et 1 serviunt prae columna prita cujascumquse pote rae
et dantperiodum e1
02 1,3, vel 0, 1, 10 H serviunt procolumna secunda
0, et 1 dant 0pro columna secunda  10 dat D pro
posentia secunda quadrati, et u dat etiam v pro
1.1
v+
polat Ida qti. Ergo columna Ida quadrati habet ubique o
tme etiam petenti Columna cujuscunque potentiae parus
habebit ubique O. pro tubo 0, et 1 dant 0; 10 dat 0
a dat 1. Ergo periodus coli2dae cybi est 0001
Et generalites, in Si potentia 0, C, et 10 Daut 0 pro
columna rda; sed 11 in col. 2 dat pro paribus 0)
Ergo habemque pro
100c
pro impa abusiada phaebemus
li Columna pro comna pro periodo parium
od stotentiarum 0000, pro periodo impariam
100
1101
1 1101
1.
10
01011
10102
10n0010
Columna 3tia investiganda est ope numerorum
000
0, 1, 10, 11, 100, 101, 110, 111, Et 0 et 1, in ea dant 0, ubique
pro quadratis eo dat 1; I1 dat 0; 100 dat 0, 101 dat 0, 11 dat (
111
a coln) Ut dat 0, fit periodus 00100000 Et sufficit 0010,
pro (ubis, 10 dat 0, 11 dat 0, 100 det 0, 101 dat 1, 10 dato, In dat D et
101001
Et fit periodus 00000100
101
101
11001
11001
LMIIIN
101001
11001
10001
e
000
000
00
100
odid

## Folio 25v — 00068255:0050
# Scan: One image of two folio pages side by side, registered by the library under both labels (also fol. 26r); this page is its left half.
# Source image: https://digitale-sammlungen.gwlb.de/content/00068255/jpgs/default/00000050.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 42 lines, status machine
O0OI111000VIII10000111100001111 = O212
000400000000000011MI IMIMMLMII = Om m
-
l2 2
M = 4
0000 00DD00006DDD 000O111100001111 = 0 n (0-4, IY 1
000011II 000V711IVOVOII 10000I, IIOVOMI OcI ∞I = O2L
D0000vLHTNMTMICCITMIII
eoDBAIUD 000VOIV0OB d 000OOVOuBMI OvDBIII WoIIII,uvo III
(02) O (0212) p datesse = 002
+
=
etO
92(02)2d  L
+
O2) p = d. tP C+p = M- 1 Ergo p = m - l- 1
Ou 12, Om 1 n = Or (011.1)  10in 1
O(((O2)2V = O2+F = O
fit l+ p = M - 1 seu p = M - l- 1
Ergo
121). m. L1
12. Om1m = Om (021
1
eL
1 la
2.
m
O2 (Ol12)2
D2
2
1
2. 1 1 ma 3omt (B (H1, 41) mul-
2 =L
n
2
= O2 (02122
=)
(O2H 12L) 3n. L - 1 = = O 2Unu ( l_j = 14) na1
nas
n
O
D212

## Folio 26r — 00068255:0051
# Scan: One image of two folio pages side by side, registered by the library under both labels (also fol. 25v); this page is its right half.
# Source image: https://digitale-sammlungen.gwlb.de/content/00068255/jpgs/default/00000051.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 34 lines, status machine
14 + 13 + 12 + 10 = N
11701 n = 0011 =02I 1 = 0414 13 =0818 et 14 =0161,6
It: IM = eM OD1Z excaus. H. 1 = D33
Ex. gr. ∞2 04 14, 016116 = 016 (O a 14) 2
6414. 037132 = 632
il iM = O2m (1l) n - 1)
seu O212. O2m 1. in = O in (O21 -l) m - l)
C+
2
O8
D2n
M +
EC
+00001111000011 110000111100001111
 0000000000000000111111111111111I
n 1 =
Ma -l+ 1 - 1
suma eader mendem prini contraria priori
O
(O2m j m) N- m) (1- n0 m) n - m)
O2 12. O2m 12 = O (O21 12l) (n 1) 2 m - L-1
O2ti 122. O
0000
1e00000000000
M - 1
2
=
Dm (O 1t  1241) (m- l-2)
O
0000000000000000 1000V111 000OII
00000000100000000 NII Y III
101
00I1
0001

## Folio 26v — 00068255:0052
# Scan: One image of two folio pages side by side, registered by the library under both labels (also fol. 25r); this page is its left half.
# Source image: https://digitale-sammlungen.gwlb.de/content/00068255/jpgs/default/00000052.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 98 lines, status machine
in numero naturali omnis columna prima habet
periodum Ol, 2da periodum 0011, 3tra 0+ 14, re presenta
sic
8421. quo 
8421
1 dat 1. seu 01 ad o1 dat 01
6191 1101 01o1 00110011
0011
10c
0201
00v0 1111
Or (01)2
l. 1 = 0110
1.2 = a4 02C
1. 4 = 04 (91)2
1. 8 = 08 (
(01)4
2.2 = n 02d2
2.4 = 04(0212)
2.8 = 00(041)
2.16= 016(0212)4
4+ = 0414
916 = 016 (0818
8.32= 632 (0818)
864. = 064 (081
omissis paribus,
quae hic  uasi
240
Aa
peregionntur
extra suam
16.a
D0(o1bq
0000H1L
04 O212
0818. 0414, 0212. a1
OOH DOVDOU0D
60000000P01(401
mentur reliqua
t
2
16. 8. 4. 2.
4)e vyt.
07b
69272 11b. d- t. 2.
644 32 + 1b. 8. 4. 2.
1. I. HBt14 +1. 2F1.
2.16,2,811-+ +2.2 2.1
4. 16, 4. 8144 142 + 4.1
8Ib +8. 484172+8.
u 2. 1b 116 1. 8, + 1. 4 1.2 + 0+
1.04 A. 8 V. D ~B
2192
A. 1b
obae
1.8
eo
0ffo 2
43+ O B 3 eis
opo2 V
quae regulariter
Deinde addentur
paria sud bcd
s
ab (9, C
columnam, sum
procedunt
ie
0
iHfonrs  04(022)
Hon ollenio qen 
16. 8L
6)
A8= 08 (012) )(5 1b + 1b. 8 + ibuf. Hb2 +16.
4. 16 = 016 (0414) 2 1. 
4. 32 = 032 (04
8.8- 081G
20414
2.2
0201 t0 10
0212
se
e
Ori
d15 1b, 1016 PB121hIBI L
+
in
101
0 +01
oob a
Ob120210110
ocvoC
si
Bi Gidovdo
e
03181o
Ose
(0)61