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# Piece: https://leibnizlegible.com/api/records/41810/text
# Catalogue record: 41810 — [Über numeri progressionis Geometricae]
# Incipit: Numeri progressionis Geometricae duplae
# Date: 1679
# Akademie-Ausgabe: AA VII (assigned, not yet published)
# Other printings: (engl. Übers.) L. Strickland, H. Lewis: Leibniz on Binary, Cambridge (MA) 2022, S. 41-43;
# Record in the Leibniz-Katalog: https://leibniz-katalog.bbaw.de/de/extended-search?id=41810&katnr=39170
# Work: https://leibnizlegible.com/work/00068255
# Title: Leibniz-Handschriften zur Mathematik LH 35, 3 B 5
# Folios: Bl. 46 (from the shelfmark LH 35, 3 B 5 Bl. 46): 2 pages, canvases 91–92, page ids 00068255:0091 to 00068255:0092
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=00068255&page=91
# Lines: 49 recognised on 2 of 2 pages, mean confidence 0.87
# 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 46r — 00068255:0091
# Source image: https://digitale-sammlungen.gwlb.de/content/00068255/jpgs/default/00000091.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 38 lines, status machine
lFL. Nua iii progressionis Geometricae duplae l. 2. 4. 8. A 6. 32. 64 Ct
sanm quia 1+2 +4 facit Y, hinc tres quilibet progressionis Geometricae Contamae termini in duplae
L
contumae termini divisibiles per 7. Nam 2+4+8 fait 14, et 4 + 8 + 16 facit 28
et 84 16+32 facit 56, et ita porro.
e
ex meo modo exprimendi Nam 1II C est Z sicundum expressionem dyadicam, et
110 seu B+4 + 1 est 7 bis et 11100 est 7 quater et ita porro.
Hinc generaliter Omnis suiama Numerorum progressionis Geometricae continuae
cujuscunque dividi potest per to summam totidem num erorum primorum
initralium inde mla seu ab unitate sumtorum, ejusdem progressionis
Et proinde duae summae totidem numerorum progressionis Grometricae
continuae ejusdem habent communem divisorem.
imo duae summa numerorum propessionis geometricae continuae potest
divisi per numerum summam numerorum ejusdem progressionis ab
untonte incipientium, si Numerus multitudo Numerorum progressionis
Geometricae dividenam com ccividendum componentium divide ex acte
potest per Multitudinem divisorem componentium.
Numerus ex summa Numerientm progressionis Geometricae continua
additis conflatus, nullum alium habet divisorem, quam sum potesta
Aliquam potestatem radicis progressionis, (per p num per hanra (quae
quatis sit ex ipso numero scri potest) et ipsum numerum primum ex
primis dotidem ejusdem progressionis conflatum, qua siqu
Cx Numeris prognessionis Geometricae
alicujus. dividi  addendo conclatus dividi potest per Numerum ejiusdem prognession
pujusque vvisores.
md adhuc amplius: quilibet Numerus
x primis Numeris seu ab unilute incipientibus ejusdem progressionis Geame-
tricae eodem modo sese invicem habentibus sive proportionalibus; et praeterea
H tum omnis Numerus ex Cujuscunque progressiones Geometricae inferiones Numeris
per aliquam potentiam progressionis.
idditis
conflari potest
conflatis per solam additionem dicendum et de umens
Omnis Nomerus qui per
flatis per mixturam additionis et sub tractionis
quod diximus de Numeris.
oeit

## Folio 46v — 00068255:0092
# Source image: https://digitale-sammlungen.gwlb.de/content/00068255/jpgs/default/00000092.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 11 lines, status machine
0
constructio Namen per fecti
Euclidea:
1I per 10 dut 1ovet 0 de ia liter I
dat 14 seu
11
11 per 10 dut 200 + 1, seu  a 11 t 10+ 1, qui sunt omnes diresores ipsa 110, si 1 est primu
an
I1 per 100 det 10900 + 100+ 100 s. .l 1 1det 184 ruisorent omnes divisnes
ipi 1+ 0gi 1 puse rupe 2ago 3+4 + 2-
seu hat MC