# Leibniz Legible — https://leibnizlegible.com
# Piece: https://leibnizlegible.com/api/records/17185/text
# Catalogue record: 17185 — Leibniz an Jacob Bernoulli
# Incipit: Gratissima mihi fuere quae de seriebus infinitis, itemque in Cartesium
# Date: 1697-04
# Sender: Leibniz — Addressee: Bernoulli, Jac.
# Akademie-Ausgabe: AA III,7 N. 088
# Other printings: -Gerhardt: Mathematische Schriften, Bd. 1-7, 1849-1863, 3 S.61-62. -Bernoulli, Jacob, Der Briefwechsel, hrsg. von A.Weil, C.Truesdell u. Fritz Nagel. Basel/Boston/Berlin 1993. S.94-99.
# Record in the Leibniz-Katalog: https://leibniz-katalog.bbaw.de/de/extended-search?id=17185&katnr=33898
# 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. 441 (PDF, Repositorium des Leibniz-Archivs, CC BY-NC 4.0): https://www.gwlb.de/fileadmin/Leibniz/repositorium-des-leibniz-archivs/III7A.pdf#page=441
# Work: https://leibnizlegible.com/work/DE-611-HS-958800
# Title: LBr. 56 · Bernoulli, Jac.
# Folios: Bl. 29 (from the shelfmark LBr 56 Bl. 29): 2 pages, canvases 57–58, page ids DE-611-HS-958800:0057 to DE-611-HS-958800:0058
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=DE-611-HS-958800&page=57
# Lines: 34 recognised on 2 of 2 pages, mean confidence 0.91
# 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 29r — DE-611-HS-958800:0057
# Source image: https://digitale-sammlungen.gwlb.de/content/DE-611-HS-958800/jpgs/default/00000057.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 150, 2026-09-10T03:45:29Z — 31 lines, status machine
Mons. Bernonlli professeur a Bale
gratissima mihi fuere quae de serrebus infinitis, itemque
in Cartesium dedisti, nondum antea mihi visa; et in C
universum quicquid a Te est, non potest non mihi esse gratissimu
pro seclbus infinitis indagandis usus aliqua ido sum
datione singulari quam exponam paucis, quia forte rectuis me
illa ut potes Reduco nempe ad quadraturam curvae, cum
alioqui curvarum quadhaturas rovocemus ad series. succedit
in munmeris, sed ulicubi nonmat haeremus exempli causa
+ + L etc. confilat
9
16
quaeritur summa lujus seriei+
eam pendere ex ista-4 +  - etc. sit aequatio
serialis ad curvam Z - X + ph - X etc = y. quae rectae
2
3
tur ad nostram in casu quo X = 1 Hinc erit = - X +X = X et = diy
Et
y = dx log. (1+X): X Interim neque du. frater tuns
4
quem consului, neque ego hactenus hauc quadraturam
(dx log (1+X): X ad aliam simpliciorem revocare potuimus
etsi generaiter possimus summare X dx log. (1+X) modo
e non sit = - 1 qui solus casus nos eludit quod si lacem
huic injursitioni accendere potes scientiam ipsam promovebis
sed literis prolixis fins tandem est imponendus
dale Vabam
Hanoverae 15 Martii 169
deditissimus
Sodefridus Guilietnus Leibaitius

## Folio 29v — DE-611-HS-958800:0058
# Source image: https://digitale-sammlungen.gwlb.de/content/DE-611-HS-958800/jpgs/default/00000058.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 150, 2026-09-10T03:45:29Z — 3 lines, status machine
implissime et Consatisime
autor
SACHSISCHE LANDESBIB