# Leibniz Legible — https://leibnizlegible.com
# Piece: https://leibnizlegible.com/api/records/41808/text
# Catalogue record: 41808 — [Aufz. zur Dyadik]
# Incipit: 9 aeqv. 1001. 16 aeqv. 10000. 7 aeqv.111
# Date: 1679
# Akademie-Ausgabe: AA VII (assigned, not yet published)
# Record in the Leibniz-Katalog: https://leibniz-katalog.bbaw.de/de/extended-search?id=41808&katnr=39133
# Work: https://leibnizlegible.com/work/00068253
# Title: Leibniz-Handschriften zur Mathematik LH 35, 3 B 3 (shelfmark LH35, 3 B 3)
# Folios: Bl. 17 (from the shelfmark LH 35, 3 B 3 Bl. 17): 2 pages, canvases 33–34, page ids 00068253:0033 to 00068253:0034
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=00068253&page=33
# Lines: 157 recognised on 2 of 2 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 17r — 00068253:0033
# Source image: https://digitale-sammlungen.gwlb.de/content/00068253/jpgs/default/00000033.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 151 lines, status machine
B 9 aequ 1001.
 aequ. - aequ
9
1001
10000 - 111
verit 1 aequ L aequ + 2
ot
00001
duorv
000
asb
9+7 aequ. 16.
Ergo per Tatae Regulam progossionisGem etricae
e
+ 4G
10,16
+ 2 +  etc.
163
165
seu: 00001 + 900000117+ 900000001100B1 + 9000VVDHZICOIBIII
00001 000001DDI
quadratum 00111 seu 0011 in 00r habet bis 5 chauderes
uno demto nempe g. Tubus habet ter 5 characteres seuts
00111 ubi patet characterem
00111
B000d
producti C.
60111 A Componi ex
010 11
01 11
00 0
(000110001
charcteribus iuli
od+I
numerochageorerum ipsius A,
7 aqu 00111
0000)
80601
vge
84d
rt
000000111
lemtibr duobus empe quadiati quatratum habet 17 charactes 00
et ita porro Ratio quia simultiplices exempli
causa 00111 in 8011I itstabit:
numerur
og
10
0000000 d’i
0000000 1100 0
00
110001
000 1
0000oovoriloo
d0, 0000010101011 1
et numero characterum ipsius B. invicem additis, demta
tamen unitate ob primum ultimum ipsius A coincidentem
Cum primo ipsius B. Et ob numerum ipsorum d.
metuendum non est meunitas exadtio aliqlua ex additione
characterum orta ultra notarum loca ad sinistram prolcurrat
Hinc in quadiato sunt novem characteres, in cubo 9+5 1
nempe  5+5 - 1 du Cubo vert (3. nempe 9+5-1 aequ 13.
qu.g.
in quadrato quadrato 17, nempe 13+5 - 1 et itapono.
Polentia
aserum cum componatur fractio degimalis ex summis nume rorum
progressionis Geometricae contimue additia; at vero Comnis continuae 
Terminorum progressionis Geometricae summa sint, etiam progressionis (imd Emus
Geometricae, hinc sequitur ipsas potentias progressionis Geometricae mo
esse periodicas id est denique in pericdum incidere. Hinc novum
quodit, et plane mitabile inventium scribendi altissimas potentias
Necesse est enim earum inotim, seu disaracte et smistras et magis
a sin str, versus dextrum eo magis esse periadicos quo magis
sunt altae. Et quando sunt polentiae fractionum cum posteri ores
characteres negligi possint, pascet quam mira mic nascitura sit calculi
Addenda hic methodus alibi tradita
in qua ex terminis, et differentiis
et differcntiis differentiarmem
itunae a ipsi teimini inveniuntu
accedentibus sumeris combina
touis
16
1647 1647,16+ 72
162
16 4716+ 3,16+
16 agu. 10000. 7 aqu. 111
facilitas pri seriibus infinitis
58
RndraE. 2
et etC ex tsrq.
Sintnundu ete d Cb a = x et et Pn mCCy
ubi duplex periodus b
01
prixyfit 1 a - l = 0 p. 1
 Nam una qu
Eadem modo paterit procedi in pluritus modo certus orto servetur.
ariqua in
Talia fiuut
reduplicatione prodeunt enim contrari
cienda cum
tiones
na
eriodi, a tota altera periodo
b habeatur
Votalis
nova perio
habebur int
in columnae primae lex in
in quadrato. idem in secundis
X- 7, quae
lesr
lolummae prime
 unus ordo sedium est ab alio in
et poterit
pinvorum ongur
21
et
sequenti ubistabi
detra tento 1 a sequenti, nullus  eut
amqui
hoc loco nons
tron ex pressio
et pro a -t sendi
faciendo ibi
ap
us
hi
ares suntut
1a-
= M - 1
syque
1
un
asse
sem
et
a, adeoque
pano
ens
pler periodus.
utque ita pergi potest ad
Nicultale
eo lam
columnam uel et ita
quod 1a = l. potest
quadrti gentralis
esse
vel 11, ergo non po aequali un
ut aequabi
cormmanter sed
stabit in columna tertia

## Folio 17v — 00068253:0034
# Source image: https://digitale-sammlungen.gwlb.de/content/00068253/jpgs/default/00000034.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 6 lines, status machine
m ec p
2
o 1
1
FRIED WILHELM LEIBNIZ BIBLIOTH
DERSACHSISCHE LANDESBIBLIOTHEK