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# Title: LBr. 57, 1 · Bernoulli, Joh.
# Folio 30v, page id DE-611-HS-958803:0060
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=DE-611-HS-958803&page=60
# Source image: https://digitale-sammlungen.gwlb.de/content/DE-611-HS-958803/jpgs/default/00000060.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 60 lines, status machine
# Lines: 60 recognised, mean confidence 0.67
# 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.

si dac
M. 1
Egm
At
B
2
2t
+
e
ea
e
d reda
dxy = X  + ydx
ad Xy = X ddy + 2dXdy + Vddx
3
Xy = Xdy + 3dx ddyue + 3ddx dy +  dX y
xy = Xy + 4 dx au +6 dx ddy+ 4ddy + d x
CA
p
et ila poro
sit
un d quae sit constans,
idem est in potus rectangulo, seu
est
producto ex pluribus, et in polysnomio
ut numeri consentiant
pro Nempe  x ponitur
L2 x+y = X +3X y + 3X  + y
pro
a Xy
d Xy Y3d Xdy + 3dedy + 41
m n
m
n
Itaque pro termino X V ponitur a XaV
nam dV = y posito n =0
In
si X potentiam habeat ut siquorratur axy
res redit ad tinomium quasi esset dxzy posito
o=X. Ebrespondebibe huic potentis
X4X +y seu l22X+y mo etiam.
M X-y et a
se
u n
A
L
u sic L26 X - y = C0
2
1 
a, X.I
2
1
=2pv  1
et
dXdy- 2aXdy H7
A Etquia sumo atiines respondent et tactur fobus
a
Imo vitendam an non c cum sm
in summationibus aliquid concipere
2