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# Title: LBr. 57, 1 · Bernoulli, Joh.
# Folio 240v, page id DE-611-HS-958803:0482
# Scan: One image of two folio pages side by side, registered by the library under both labels (also fol. 241r); this page is its left half.
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=DE-611-HS-958803&page=482
# Source image: https://digitale-sammlungen.gwlb.de/content/DE-611-HS-958803/jpgs/default/00000482.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 45 lines, status machine
# Lines: 45 recognised, mean confidence 0.94
# Machine transcription. Not an edition. Errors are expected: about 8% character error rate on Latin and French lines, higher on German.
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# After the first blank line: the recognised lines in reading order, one per line.

hotet gravitationem particulae FC reliquurumque omaium quae
sunt in eadem profunditate seu quae sunt in rerta GC prolongata.
pariterqe cum singulae religuarum applicatarum DE denoteat
gravitationem particular Mx caeterarumque quae suint in rerta
applicaba
prolongata EMI: Omaer ulique partientu simul sumta hoc ert spa–
fia BLG, BDE designabunt omnes gravitationes (non duo gravi
Lates) simul sumtas particularum quae sunt in filamentis DFC
pN. Ideoque sifiat alia curva BH cujus applicatae GF
sint ut respective spatia BLG; atque si ad S appliceatur 83=G.
Labebitur nova curva B2N, cujus applicatae P2 exhibebunt
sumat gravitationum particularum in sunt respertive fulamendis
DFC; et proinde suma applicatarum P2 id em totum spatium
B2N repraesentabit gnravitationet omnes omnium particularum
fotius liquoris linteo BFK contenti. Siquidea igitur linteum
tatem capiat figuram ut gravitationes omnes simul sumta
hoc eit spatium BNZ faciat maximum. Evidens ulique ert
si adhiberetur liguor gravitatis continue diffortuir hac lege ut LG
DE seu gravitationes particularum in profunditate F, M esceat
in natione differentialium applicatarum HG (quae scilicet in pro-
blemate fraterno designant funitiones iprarum PF) evidens
inguam eit, quod tunc cuvatura liater exhriberet eama ipiam cur
vam, quam trater pro potertatibus tantum ipraum PF mihii
quareadam proposunt, ego vero generaliter pro quavis funitio
ne per methodum directata resolvi. Ut igitur hujus methodi
dirertae cum indirerta consentum demonitian, placet indagare
naturam curvaturae linter a liquore ea qua diciratione gravi
dationes variante onerali, quod si in eandem incidero aequatio
nem supra inventam, quis cquaso de intallibilitate methodorum
func dubitare audent Hic quidem itatia occurrit casus
facilimut qui primo diientiendus ett, nempe si liquor sit ordi
narius seu gravitaris unifurmis soc est Li gravitationes
LG,DE sint ut ipra profunditates BG, BE; adeoque linea BC
Et recta, et BH parabola comunis: Tunc BFK erit ordinaria
curvatura liatei quam etiam frater suae elarticae tribuit quaque
exprimitur ut jam olim reperi conveniente fratie per hanc aequa
tionem y-
sd: Jam vero Liin aquatione generali s dirertam
Vatt -X E
methodum supra inventa is
CXd
ponatim loco generalis fumtio
saa-X
nis X cacus particularis xx qui am supponitur, provenit y-
Naanxt