# Leibniz Legible — https://leibnizlegible.com
# Piece: https://leibnizlegible.com/api/records/15446/text
# Catalogue record: 15446 — Leibniz an Johann Bernoulli
# Incipit: [fehlt] Unde Tibi deliberandum relinqvo ... facti sint ejusdem serici
# Date: 1695-03-10
# Sender: Leibniz — Addressee: Bernoulli, Joh.
# Akademie-Ausgabe: AA III,6 N. 101
# Record in the Leibniz-Katalog: https://leibniz-katalog.bbaw.de/de/extended-search?id=15446&katnr=45218
# AA III,6: 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-6
# In the Akademie-Ausgabe: AA III,6, p. 383 (PDF, Repositorium des Leibniz-Archivs, CC BY-NC 4.0): https://www.gwlb.de/fileadmin/Leibniz/repositorium-des-leibniz-archivs/III6A.pdf#page=383
# Work: https://leibnizlegible.com/work/DE-611-HS-958803
# Title: LBr. 57, 1 · Bernoulli, Joh.
# Folios: Bl. 26r (from the shelfmark LBr 57, 1 Bl. 26r°): 1 page, canvas 51, page ids DE-611-HS-958803:0051 to DE-611-HS-958803:0051
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=DE-611-HS-958803&page=51
# Lines: 46 recognised on 1 of 1 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 26r — DE-611-HS-958803:0051
# Source image: https://digitale-sammlungen.gwlb.de/content/DE-611-HS-958803/jpgs/default/00000051.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 46 lines, status machine
Unde Tibi deliberandum relinquo annon pro integralibus vestris prastet
imposterum uniformitatis et harmonia gratia non intor nos tantum, sed
et in ipsa doctrina, adhiberi summatorias expressiones ita ut ex. gr.
Sydx significet summam omnium y in de respondontes, suctarum, seu
summam omnium huiusmodi rectangulorum p praesertim
cum tali ratione
summationes Geomotrica seu quadratura optime cum arithmeticis seu
serierum summis conferantur. Nolim tamen vobis praeseribere quicquam
sed tantum ejus quod maxime rationi consentancum videbitur putem
rationem maxime habendam. Ego certe in totam hanc methodum me fa
teor ex hac consideratione reciprocationis intor summas differentiatque
incidisse et a seriebus numerorum ad linearum seu ordinatarum conside
rationes processisse.
Unum addam quod etiam hanc reciprocationem confirndat, si ponamus
m’aqu. 1. m esse numerun negativum seu m =-,
ex aqu. 1. fiet, (posita de = 1) see pr  ge
(nt2. p -C
fore dm et
ee, unde
S.M e.  srH
n  ZC-2
n, eto semper  tamen series tales infinitas ea
decrescere intelligendum est, ut termini continuando siant quibus vis
datis minores.
Ad tale artificium opus est, ut duo termini ex unius differentiatione facti sint ejusdem
teriei
X = y A C Slyu = v sar x Et dyius - xvia  hostax seu ly - 1 X v + du Slx: X. X
dxg  Aex gex Xy= 
X
a=
se-
dnisa
ec 
e
a-b
st
W 13
X 4 X X ) X 7
vi
a =
Saro sode +sedsate 
a =  atb boc + ctd - d- e et
Hec utile ubi duo talia quonunt aliquid sum abile ut in easu pa
praecientis
Nempe quando cunque repenitur series   in qua duo termini proximi
certa lege sumti, summabile coporunt