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# Piece: https://leibnizlegible.com/api/records/16796/text
# Catalogue record: 16796 — Leibniz an Johann Bernoulli
# Incipit: Litteris ad Te dimissis mox in mentem venit oportere
# Date: 1696-11-19 (96-11-09)
# Sender: Leibniz — Addressee: Bernoulli, Joh.
# Akademie-Ausgabe: AA III,7 N. 047
# Record in the Leibniz-Katalog: https://leibniz-katalog.bbaw.de/de/extended-search?id=16796&katnr=45232
# AA III,7: the volume in the Repositorium des Leibniz-Archivs (CC BY-NC 4.0): https://www.gwlb.de/leibniz/digitale-ressourcen/repositorium-des-leibniz-archivs/laa-bd-iii-7
# In the Akademie-Ausgabe: AA III,7, p. 262 (PDF, Repositorium des Leibniz-Archivs, CC BY-NC 4.0): https://www.gwlb.de/fileadmin/Leibniz/repositorium-des-leibniz-archivs/III7A.pdf#page=262
# Work: https://leibnizlegible.com/work/DE-611-HS-958803
# Title: LBr. 57, 1 · Bernoulli, Joh.
# Folios: Bl. 104 (from the shelfmark LBr 57, 1 Bl. 104): 2 pages, canvases 209–210, page ids DE-611-HS-958803:0209 to DE-611-HS-958803:0210
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=DE-611-HS-958803&page=209
# Lines: 75 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.
# 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 104r — DE-611-HS-958803:0209
# Source image: https://digitale-sammlungen.gwlb.de/content/DE-611-HS-958803/jpgs/default/00000209.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 39 lines, status machine
et) 1tX
Vir (. eleberrimi sautor
Hlonoratissime
iteris ad Se demissis mox in mentem venit oporter
ut error in illis admissus fuerit. Nam area illa
quam aequalem feceram seriti de qua agitur infinita
est sRe ergo resumpta vidi sic procedendum
L + X
7
+ X + X etc = dy. Unde Z + XE, X3LX+
Ergo dus = log.
2t
9 16  y
1=X dx. Seu y = ( log. 1 = X
dx
sed cam log. 1= X sit infinitus, eo casu quo X = 1. ideo
patavi commalius rec accedi posse, si pohibeamus
L- L + L =  eto. FCamheperio hac summa data
4
c
etiam haberi suemmam= + L + L +  etc. Iaq aessumo
L - X1
2
+ X2 CX3 etc. = dy unde X - XE, X3d Y4
16 etc = y
umus X = XE, X3 Xt4
et Sit log. 1+ X, utique patet
fore dy = log. 1 + X dx seu y = . log. 1+ kQ Rexeri
autem generaliter esse S. Xe Logar. 1 + X da-
e
VE
ut
a
ets
da Etfatum singulare naturae caurione
a
accidit, ut in unieo nostre casu ret non succedat, eam
scilicet fit c = -1 tuncenrm L - L quae est quantibas
infinita. unde subsidlia summationis evanes cunt

## Folio 104v — DE-611-HS-958803:0210
# Source image: https://digitale-sammlungen.gwlb.de/content/DE-611-HS-958803/jpgs/default/00000210.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 36 lines, status machine
Nondum harctenus occurut mihi alia ratio qua-
Sitam y inveniendi. Analiunde pateat aditus tu
optime clispeneus
Si fumma haec aurdatur perx, et quod provent
rursus summetur, prodit summa pheborum et sicum
hat procedatur codem modo procit summa biqua-
draticorum et ila porro.
Flabemus ergore
recuctionem secierum adsuas quaedtraturas sal ipsa
Hoc loco quadraturae adhuc deriterantur. Interim
ipiam methodum aggrediendi series non aisplici-
uram pueto, cum aese resad quadraturat qua
in postestate sunt heduci possit exemplicaura
2ite 3,2+8 4sc et. Sempter habeui
eries 
C
+ L
potest, modo esit memerus major unitate, quod
ea peracedentibus patet, quia sit si X C. = + X d+
si
e
- XC+1
C 2. ei
 k.
C+2 X
C = 2
eti. Quad semper habere
2, et 2 4, ex 3
haben potest Eacepto casre, quo c =- 1. quanquam
C
fortasse et in hoc casu habebitur tua ope accedente
Haeraptim sercoribus subinitere volui, ne sibi
hor calculi à me dormitante nescio quomodo
ninosus soustra negotium facesseret
ale cabam Hannoverae 9. octobi. Sbg.
ad du. I0E. Bernoullium proningam