# Leibniz Legible — https://leibnizlegible.com
# Piece: https://leibnizlegible.com/api/records/55186/text
# Catalogue record: 55186 — Leibniz an [Overbeck]
# Incipit: Cum nuper forte dyadica recogitarem,
# Date: 1714
# Sender: Leibniz — Addressee: Overbeck
# Record in the Leibniz-Katalog: https://leibniz-katalog.bbaw.de/de/extended-search?id=55186&katnr=36905
# The Leibniz-Archiv's transcriptions of the letters of 1714 (pre-edition): https://www.gwlb.de/leibniz/digitale-ressourcen/repositorium-des-leibniz-archivs/laa-transkriptionen-1714
# Work: https://leibnizlegible.com/work/DE-611-HS-861255
# Title: LBr. 705 · Overbeck
# Folios: Bl. 69–70 (from the shelfmark LBr 705 Bl. 69-70): 4 pages, canvases 137–140, page ids DE-611-HS-861255:0137 to DE-611-HS-861255:0140
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=DE-611-HS-861255&page=137
# Lines: 249 recognised on 4 of 4 pages, mean confidence 0.72
# 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 69r — DE-611-HS-861255:0137
# Source image: https://digitale-sammlungen.gwlb.de/content/DE-611-HS-861255/jpgs/default/00000137.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 54 lines, status machine
3 B O B
11001102
11007700
Tomio roc. sua
1ne1l00+0148
ato
 2E = 1 + 2 +b18 +
-
-
l
12
V
+2
E + 11 + RF b + 2 +1
t9.
= 2E = 91 + R + B + 2
91
8t B + 2 +
Vir Clarissime et dostissime
l
Amice honoratissime
um nuper forte dyadica recogitarem, anima
dati
verti generaliter, notas numeri ayadicas inno descerx
si continua ejus subdivisione per mediationem facta,
dividendis paribus ascribatur 0 imparibus l. Ex. est
O
d
1
1D
D 
O101 F13
41
lS
lidem dividendi qui continuas mediatione prodeunt
sunt etiam quotientes divisionum ejusdem Numeri dat
per 1, 2, 4, 8, 16, etc.
∞ X r
+
 1
dua
d
3 1 0 10 11 133
e
d
c
3
2
proposica antem serie, in qua ordo notarum
dyadicarum columnatim quaenitur considerandu
eut ordo paritatis vel imparitatis in quotientibus
terminorum seriei per eundem diviserem dyadicum
productis. Ex. gr. in quadratis
2

## Folio 69v — DE-611-HS-861255:0138
# Scan: One image of two folio pages side by side, registered by the library under both labels (also fol. 70r); this page is its left half.
# Source image: https://digitale-sammlungen.gwlb.de/content/DE-611-HS-861255/jpgs/default/00000138.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 67 lines, status machine
O
L
2
en
9 1b
L
4
2
l 2
0n 6 1
25 363493647
4
8
4
L
2
a
Ibm
6
3
6
31
8320c
4
10
0
50
d 12 16720 25
2
2
2
l 
e
12
ubi patet differentias quotientum esse numeros
progressionis Arihmeticae sed sub peculiari quadom
ege repetitionis quae eruenda superest.
X = 2(X) 4a (X = 00112233 ek a = 010101 ex
0 1 4 9 16 25 36 ) = A(X) + 2b +a, ubi X (2(X) - 0000mnu 3273 ex fteF
0 0 2 4 8 12
0
0
1
2 C
0 6 0. 1 2
XX = a 4 (XX) + 4() ataa
cumvana
((V)a 4ba
cujus in quarta maxmms integer est par
Si tam b quam a sit 1, item si b est 0, seu 5
seu ei lorba est par
X = BB() + AC + 2b + a
a
XX = 64 ( (XX) +64(3(X) (4C + 2b + a) + qu (4 c+ 2b t a)
cu
cujus ata est par si b Acarabta sit par
16C + 161∞ + 4
8xa aa
18
10
+
4
2I2
Z((2(XX) l00 0
2 (2(X)
(X) a
2 3

## Folio 70r — DE-611-HS-861255:0139
# Scan: One image of two folio pages side by side, registered by the library under both labels (also fol. 69v); this page is its right half.
# Source image: https://digitale-sammlungen.gwlb.de/content/DE-611-HS-861255/jpgs/default/00000139.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 72 lines, status machine
100 (21
10
5
6c
30
25
27
144 169 196) 225
l 
30
18
2
33
49c
42 49 Y
X = 2(X) ta ind
+
3
n2
l2
56
24  2e4
int. in
a
e e
5
a  6, 1 4, 0(B1 R, 0 WI
H2
a b = 0010On ex a= 01OIO1 etC p ((X) = 2 (7) +b jad e p
fisa  ((X) 0 0 00
C
3
3 (4 4
O) 1
Ol 10
ael5
1 0 0 1 1 001
a b110 1 ac
256
12
0
64
X est o
= 99 1011 12 13 14 15, 16,
e
40_ 1(XD(BiL (R L
c
= (4 (X) + A _) + a = 2(XX) + 3()
(  XD +1 fit aK) 13
X H = A(X) + 2(X) +1, A et X = 16().
X
5
(050
0
stot
1
3
o
1 0 c 01 01 01
0
(
9 16253649 64 8) 100 12) 194 169 196 225 256
4 9 112 128 est semper par
 CX_ 0 0 1 2 4 8 9 12 16 20 25 30 36 42 49 5664 est pcum  pa (X) est
12
H  6 0 2 4 8 13 18 2 32 40 50 60
cmpar C si b sit d, vel si b e a sit 1 ensilbiba
4 6 8 10 12 15 18 21 24 28 32
Pa
X est dimidrum maximi
a est ovet 1
paris in numem contenti

## Folio 70v — DE-611-HS-861255:0140
# Source image: https://digitale-sammlungen.gwlb.de/content/DE-611-HS-861255/jpgs/default/00000140.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 56 lines, status machine
someunti in ah iaz. sinemo
ep utsinis inpuno in 10no) lumevimani
ugm ant li Sipounum hoc syviror apra
epuveisod rustitob inuum caurou
lunse  0
puB
as nit in rrans lurgur vorse
851 11
0 1 0 1 0
e  n e - D ea e.
e
4 1 ∞ f e -
= e t ∞ e
ce e
d g1E
B 2 I es
mmns metut lumioisiere Sohuect vs pump
gundeeri surquis utvumrum cab luopiate imopi
6EL1
10 16) O
v u ea e  Ona C
4 r∞ et e 
e
eb. 22.1 tugumtum p intrapriso sugroi semae
ulsvengue int gueciegus sut mogu i
atgsp euvisp eoro nonuu njeri appngure qu
uu
victur mnns heror mgone dues nomo uo
dmissurnm nass
duississ  dmisurv,) M
e
e
1+ 2 + 418 = 16 - t
1. + 2 +4 + Y + 16 = 32 = 1.
1 + 2 + 4 + 8 + 16+3 = 641
AB3, = 2- 1
2+ 1 = 4 - 1
F 2 + 1 = B
+B4+ 2+1 = 16- 1
96 + 819+ 2 + 1 =
32 - 1
C
10000
p
1000000+001100H
an
Axextarai
120
quod. et divis. dat ormnreh
001001)
O1
v6 +10e11
110
1e
ete
1. 0 00000