# Leibniz Legible — https://leibnizlegible.com
# Piece: https://leibnizlegible.com/api/records/19219/text
# Catalogue record: 19219 — Leibniz an Overbeck [?]
# Incipit: Venit nuper in mentem facilius fortasse perveniri posse ad dyadicam po
# Date: 1712
# Sender: Leibniz — Addressee: Overbeck ?
# Record in the Leibniz-Katalog: https://leibniz-katalog.bbaw.de/de/extended-search?id=19219&katnr=35760
# The Leibniz-Archiv's transcriptions of the letters of 1712 (pre-edition): https://www.gwlb.de/leibniz/digitale-ressourcen/repositorium-des-leibniz-archivs/laa-transkriptionen-1712
# Work: https://leibnizlegible.com/work/00068207
# Title: Leibniz-Handschriften zur Mathematik LH 35, 15, 5
# Folios: Bl. 10–11 (from the shelfmark LH 35, 15, 5 Bl. 10-11): 4 pages, canvases 17–20, page ids 00068207:0017 to 00068207:0020
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=00068207&page=17
# Lines: 113 recognised on 3 of 4 pages, mean confidence 0.84
# 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 10r — 00068207:0017
# Scan: One image of two folio pages side by side, registered by the library under both labels (also fol. 11v); this page is its right half.
# Source image: https://digitale-sammlungen.gwlb.de/content/00068207/jpgs/default/00000017.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 23 lines, status machine
yso
dir clarissime, fautor et finire
nonoratissime
denit nuper in mentem faciluis fortasse
perveniri posse ad dyadicam potentiarum expressionem
det Geometricas propessiones yadice expressat. Nam
Dgadicae expressiones odeunt ad Residua divisionum
per numeros progressionis duplae. porro Residua
numerorum progressionis Geometrilae rationalis integrae
cujuscunque pecularia e pulchia dare compendra
nosti et si nellibnur cujusque naturalium pro radicesumto
habeatur propressio Geometrica eo ipso omnes aturatium
potentiae habentur
+ 256 1074
Modum dyadice scribendi 1, 2, 4, 8, 16 et per se habemus
C
sunt enim 1, 10, 100 1000 10000 en. Modus autem
radice scrbendi 13, 9
squaerantur herum residui primuma
ab 8, decude a 16, et Ila porr.
habebiti
2 Deinde a 4 deinde
43

## Folio 10v — 00068207:0018
# Scan: One image of two folio pages side by side, registered by the library under both labels (also fol. 11r); this page is its left half.
# Source image: https://digitale-sammlungen.gwlb.de/content/00068207/jpgs/default/00000018.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 42 lines, status machine
Exponentes
Numeripras
domtrie
divisores
+
(4)
E3
d
19bE
59e
9
ibi in investigandis resicuis
Id commodi habemus
quod suppeditant Numeri progressionis geometricae per eundem
civisi, ut scilicet quaedam quasi Logarithmica lex observetur
e difficulter fresidui sequentis divisoris, a divisore residuri
praecedentis derivantur. Et quod in divisn dividendis progressionis
triplae dedimas, etiam haberi poterit in dividendis progressionis
tequadiuplae, quintuplae etc
porro ex resionis hujusmodi habetur expressio dyadica
Ex. g. quaeritur quomodo scribatur 243
quia residui e dyadice
expressi 10x
2
t sunt
A
1
40D 1
110011
11001I
29
115
l1D1001I 243
ita patet novi divisoris residuum, refinere notas praecedente,
prioris residui.
por ex lege resituorum habemus processum in unaordine
respducrum, quasi logarithmicum. Huic addendae est lex
transitus de ordine in ordinem v.q ex residuis ipsius 32 ad
residuos ipsius e4.
Haec pendet a quotientibus divisionum
per
12

## Folio 11r — 00068207:0019
# Scan: One image of two folio pages side by side, registered by the library under both labels (also fol. 10v); this page is its right half.
# Source image: https://digitale-sammlungen.gwlb.de/content/00068207/jpgs/default/00000019.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 48 lines, status machine
es
MM
MM
ek
l
et
M
per 32. empe quotescunque quotiens esterument
divisionis per 32 est numerus par, servatur idem
residuus in divisione per 4. sed si quotiens divisionis
per 32 sit numerus impar.
func ad residuum ejus
addi debet 32 ut habeatur residuns divisionis ejusdem
+0s)
1700d
magnum hic adjumentum spondet. Nec opus est hic
ipsos quotientes haberi ut sciamus pares sint an impares. Nam
u plocessibu poterit enim ejis rei lex, haber. Ut hoc loco cum
sed ctum dividuntur.
ex 4. sdditur atternis nunct0 nunc 8. Et semper
suplicato addito, ubique 1. sed euu dviduntur perer suut
+
 384 1093. 3280 904
0 1 4 13 40 121 364 1093 3280 9841 29529 88573
0 0 2 6 20 60 182 546 1640 4920 14762 49286
0 0 1 3 10 30 91 273 820 2460 7381 2243
0 00 1 5 15 45 136 410 127 3690 11071
00 0 0 2 7 2X 68 205 615 1845 5535
superior
gas
Addendi ad priorem plicatum
1. 1. 1. 1, 1 et pares impares
0. 2. 0. 2,02 etC. pares meri
ts
impriles
0. 0. 1. 2. 0.0. 1. 2 etc
9. 0. 9. 2. 1. 1. 2. 1. 9.9. 9. 2. 1. 1.2. 1
quEt putem leges quotientum Constitui posse sattemrulappareat, qui
pales qui impares, de hoc enim hic potissimum agi videt
tunc.
Nam polio quolieps est par, seu residuus superior repetitur,, in columna sequente
syadica ponitur 0, sin minus 1.
Quolientes
pr2
per 4
per 4
per 16
per 32

## Folio 11v — 00068207:0020
# Scan: One image of two folio pages side by side, registered by the library under both labels (also fol. 10r); this page is its left half.
# No recognised text on this page (recognized).