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# Piece: https://leibnizlegible.com/api/records/36676/text
# Catalogue record: 36676 — Ouverture nouuelle de nombres multiples, et des diviseurs des puissances.
# Incipit: (1) Numeri deinceps ab unitate ordine
# Date: 1676-01-03
# Akademie-Ausgabe: AA VII,1 N. 086
# Record in the Leibniz-Katalog: https://leibniz-katalog.bbaw.de/de/extended-search?id=36676&katnr=Cc2+1253
# AA VII,1: its series at leibnizedition.de: https://www.leibnizedition.de/de/reihen/reihe-vii/
# Work: https://leibnizlegible.com/work/00068014
# Title: Leibniz-Handschriften zur Mathematik LH 35, 4, 17
# Folios: Bl. 7 (from the shelfmark LH 35, 4, 17 Bl. 7): 2 pages, canvases 13–14, page ids 00068014:0013 to 00068014:0014
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=00068014&page=13
# Lines: 87 recognised on 2 of 2 pages, mean confidence 0.82
# 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.
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# 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 7r — 00068014:0013
# Source image: https://digitale-sammlungen.gwlb.de/content/00068014/jpgs/default/00000013.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 73, 2026-08-27T15:28:38Z — 64 lines, status machine
numeropum
3 Jannar 1676
ouverture  touvelle a0 stnm res
de Nombres Multiples, et des diviseurs des puissances.
Aditus ad novam contemplationem de Numens multiplis per eoum dispositionem et punctatione
Numeris deinceps ab unitate  ordine naturali dispositis, secundus quisque est binarius sive par
tertius quisque est ternarius quartus quisque est quatemarius; et ita porro; et generaliter appellando
numerum  N. b quisque est bnarius. Ntus quisque est Nrarius
 1. 2. 3. 4. 5 6 7. 8. 9. 10. T1. 12. 13. 14. 15. 16. 17.
secumdus quisque
Ecitius quisque
quartus quisaue
qati:
quimus quisque
Obiter notetur, quomodo omninusta puncta seuper in linea in rectam cadant, quomodo angulusemper
frat obliquoor. Quod primus est, quam per omnes inferiores numerando nunquam cadit sors.
S Corill. si numeri non pri est alia quam per unitars nnc
2) Ex duobus nameris contionis alteroter est par seu binarius Ex inter tres numeros continuos aliquis est ternarius;
innter quatvot numeros continuos aliquis est quaternarius. Et it. a porro.
(6)
Quoniam enim N3 quisque est Nrarius, et vero inter N numeros continuis unum necesse est occurrere
qui sit NH pr Numerum N. itaque unus inter eos est numerarius
Hinc factus ex aliquot numeris continuis dividi potest per numerum dumerorum continuorum.
quoniam aliquis ex ipsis ex th. 2. per ainnorum numerotum contimurum dividi potest. Ergo
Factus ex aliquot nuneris continnis dividi potest  per factum ex totidem numeris continuis deinceps ab lmita
et factus ex omnibus
panceribus
Nam  factus ex aliquot numeris continuis dividi potest per factum ex p aliquot eqs
continus ex ipsis, ergo at hi per numerum ipsorum.  p3; Ergo et ipse per numerum eorum, ergo per tit numeros
quotm panciores in eo summi possunt factores contrum id est r totidem numeros continuos
 in producto continnorum Productus excerto numero continuorum dividi potest per potestatem a 2. (vel 3. vel 4et)
deinceps ab unitete
siio exponens sit quotiens numeri continuorum per 2. (vel 3. vel +. ec). divisi omisso residuo. Nam in
tot factores resolvi potest, quorum quilibed dividi potest per 2. vel 3. vel 4 etc.
quotiue
(10)
Summa vel Differentia duarum dignitatum corradicalium est par. Nam si radix est par etiam dignitates
erunt pares. summa autem vel differentia parium est par. Sin radx infar, etiam dignitates impares. Summa autem
 YL  vel yCy+1. vel y +1 Eyt2. est par. per 3.
vel diffecentia mipatium est par
ytIgAAye3 H V+ y+ 1 y + 14, 3. est senaris per 5
sive y +3y + 2
13
 st
11 V + 6
ergo y +67 + 12Y +6 senaius.
quadrat omnis est ternarius aut unitate nenjor ternarius. Nam Y-y ternarius per ti8. Ergo vel y est ternarius vel
Ergo V- Y senarius.
non. si y. est ternarus. Eequea quadratus ejus ternarius. si y non est ternarius. Ergo quia V cyternarius erit y - 1. ternarius.
Ergo est  ternarius +1. Ergoquadratus quilibet yt, aut ternarius aut major ternario unitate.
3 + 10)) + 1222, 11) y + 12, 3 87
+ 1e2 3
35
+11213, 24 H
+ 1294
in saisas
2B.
vl y
quatenarius
50y + 12, 3, 4. Y y 41oY435 Y 4501) + 24  est Quateotius
Ergo y4 4 1y - 1 + 2y quaternarius
rem y + 513 + 1y + 6y quater narius Ergo addendo 2y2+ 8Y + 10γ +8Y.
blu
18. 19. 20

## Folio 7v — 00068014:0014
# Source image: https://digitale-sammlungen.gwlb.de/content/00068014/jpgs/default/00000014.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 73, 2026-08-27T15:28:38Z — 23 lines, status machine
s
H2
-
E
B
S
2 1
91
F2
11
15
 2
a
2. 
at
E
E+ q
ds
res
2 E 49
8 bls EH 5
D) 8
= 8