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# Title: LBr. 56 · Bernoulli, Jac.
# Folio 29r, page id DE-611-HS-958800:0057
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=DE-611-HS-958800&page=57
# 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
# Lines: 31 recognised, mean confidence 0.90
# 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: the recognised lines in reading order, one per line.

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