# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/DE-611-HS-958800:0029
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# Title: LBr. 56 · Bernoulli, Jac.
# Folio 15r, page id DE-611-HS-958800:0029
# Scan: One image of two folio pages side by side, registered by the library under both labels (also fol. 20v); this page is its right half.
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=DE-611-HS-958800&page=29
# Source image: https://digitale-sammlungen.gwlb.de/content/DE-611-HS-958800/jpgs/default/00000029.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 147, 2026-09-10T03:30:10Z — 79 lines, status machine
# Lines: 79 recognised, mean confidence 0.89
# 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.

20
- 2, d p segus. ab ad
C
31
40
subitituant, 10.=- etc. e ita
l.30
consequenter usque ad 100 adeo ut suma terminorum ab ad 100
+ L + 1 + = +
1 + 1
+  = A- 1
101
fiat
jurto major. Eadem ratione
ponant psingulis terminorum ab ad tatidem
ab2 ad
100
tatidem
100
200
et psingulis
200. atque ita porro usque ad; quo parto suma
10vo
terminorum ab ad fiet ut antea = A-  jurto quoque major: ideaque
101
100o
suma amniu mille terminorum ab unitate fiet A+ A-  + A-= - 3A
4+9 jurto major. Herum p terminis ab ad ponant toti
840
20
dem, et pterminis ab ad totidem etc. ut ep terminis ab
10
et
30
101
ad totidem: d ab ad- totidem. etc. qua ratione suma
200
terminorum ab
300
201
300
100 siet + + 1+
4
5
+ +
1 + 1 +1 + 1
=A- 1, quanta quaque ert suma terminorum ab ad
101
1000
E
10
B
jurto minor; unde et suma omnium mille terminorum abtinet A+ A-1
+A- 1 = 3A - 2 = 6 661 jurto minor. Vera ergo suma pragresrionit
340
cadit inter limitet 849.
c.
840
4 6
661
840 1
Imo inter medium horum Arithme
ticum  577 et minorem 6061 cum ortenu facile sit, sumam veram
840
840
praprui accedere debere limiti inferion quam supenon. Et certum est,
Tuae progressionis additionem perquam plurimos terminas continuam
dam este. priusquam limitem hunc asequatu: praeterquam etiam quod
nullum limitem in excessu suppeditare potert. Veruntamen uta omnia
ad Praxin parum subsi du afferre postunt.
Circa Controveniam Synamicam mentem Tuam ita nunc
demum explicuisti, ut facile mihi sit perspicere, ubi error lateat.
Nis quantitatem virium artimandam esse ex quantitate effertiis,
id ett, ut explicas, ex numero elastrorum, quorum tentione absumunt
Non repugno. Supponis item, corpus du plâ cum celentate sursum
niten
ponan
+
200