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# Page: https://leibnizlegible.com/page/DE-611-HS-958803:0221
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# Title: LBr. 57, 1 · Bernoulli, Joh.
# Folio 110r, page id DE-611-HS-958803:0221
# Scan: One image of two folio pages side by side, registered by the library under both labels (also fol. 113v); this page is its right half.
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=DE-611-HS-958803&page=221
# Source image: https://digitale-sammlungen.gwlb.de/content/DE-611-HS-958803/jpgs/default/00000221.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 37 lines, status machine
# Lines: 37 recognised, mean confidence 0.78
# 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: the recognised lines in reading order, one per line.

ii Emplissime ate celeberrime
fautor honoratissime.
Utmsque taas uno cocemque cisore accepi; in posterioribus recle
1c 10
correxisli, quem in prioribus commiseras lapsum. Sum eram, se non in-
vito id cliicerim, in similibus fere speculationibus, hunc altem matoriam
sam a longo tempore deserut, ut pene exiderit olid super cà prae-
fliterim.
SLaversaria mea desuctiens hoc reperie. In Misesbola
ABCD, si AB- BC= B 1, scet CM- satio hispeto: est C3
vero
BC
d suc ubisi; en- satio tupa: e BCF de sc ubbigte; erit spatioa
B0
ABLN = + + = +  + is dec. sl spatilon vero aB (n erit = vit
LZt; = ib c. Dnalerca sratitm BL N eit cuslum spatir
aBL2. e par cnscguens, quod note notasli, cata summa +--
+  = is d habetui etiam summa 1+  +  +  dc. Haec enim illeus clupla est.
auod scullerius spatia BLE d BEme appilicentur ad BEd Be proclibant
nova sutia quro cubis  + s + 27  Z2 dc. & + =  + 27 6q XC: e ita porro pro
e
biouacaticis. Quamris autem omnes istae series sint insummabiles, possum ta-
en non ineleganti quodam artificio illes dispescere in pastes datam habertes
rationem, sic series generalis potestatis numeri n est huc  + n +  + gudes
multiplicatis numeratoribuls d aenominatoribus per datum numerum ad n ele-
2
a
valum ex: Gr: p 22 erit  + za + n +  dc: = 2 1 n 1 a +.
e
est
2. in t qu + in t on Bc: est ego summe terminontm imparium in t, a + ser + qa c:
ael summem parctem a +  + n L one dec ut 2 min 1acli. &t proiiacle, k + in + ,n
qa d acl jn Z + n in dc: ut 2 adt 2 2: hine palet quod supra onnui Cexi-
stente scilicet n =2) summan , + + +
1
16 _ci esse duplam summue
Xc. Hinc dum altio segiitus summam hamonicorum esse in-