# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/DE-611-HS-958803:0481
# Permalink to this reading: https://leibnizlegible.com/page/DE-611-HS-958803:0481?run=74
# Title: LBr. 57, 1 · Bernoulli, Joh.
# Folio 240r, page id DE-611-HS-958803:0481
# Scan: One image of two folio pages side by side, registered by the library under both labels (also fol. 241v); this page is its right half.
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=DE-611-HS-958803&page=481
# Source image: https://digitale-sammlungen.gwlb.de/content/DE-611-HS-958803/jpgs/default/00000481.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 40 lines, status machine
# Lines: 40 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.
# 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.

Scholium
faud major difficultate hac methodo determinare possemus
e
curvam BF_, si denderaratur ut PZ (fig. J.) escet funitio compo
sita prolubitu exfunitionibus non arcus tantum BF vel applicatae
et; sed utriusqe simut quomodounqe inter se complicata. Eo enim
tandem semper pervenitur ut sirus curvedinis in quovis punitot
sit ad certam quandam quanditatem in ratione conclante; unde
problemate hoc modo ad pure analylicum redarto, facile deinde
aequatio naturam curvae exprineat obtinetur. Hac eadeta methodo
solvi eliam possunt curvae calenariae ut et brachydochrona, qua
rum onniuu solutiones egregie conspirant illis quas olim divercis
methodis caventas dedimus: id quod non parutu eujus methodi
bonitalem comendat.
caterum cun hac direrta sit placet adjungere indirertam
a natura prescionis liguorum desutntam, qua eandem omnino
dabit solutionen; quo methodorum direrta et indirertae tam
in rabili conseatur iinrifice contrimabimur de illarut certitudi
he. Etto (Fig. T.) BFN lintenn a liquore iagnante uniton
ic sive non unitormis gravitatis expaunm, condeas est illud
eam induere curvaturat, quae liquom maximum concedat descen
tum: Hoc autem lunc continget, quando omnium particularum
totius liquoris gravitationes simul sumta faciunt moxisnum
N non dico quando centrum gravitatis liquoris et in infimo loco,
hic enim non potect considerarn centium gravitatis, siquidem va
rianle curvitura BFN licet cropermetra, variat Lamen etiam
ipsa quantitas ciguoris sub illa contenta, adeoque non escet centrum
gravitatio uniu ejusdemque liquoris;) gravilatio autem particula
cu povis aclimatur a pondere incumbeates filament: liquoirs,
per graculationem itaque intelligo vim qua superficiet aliqua
imaginaria in liguore hori donti parallela ab incumbentis pondere
deortum urgetum. Jam vero dirtiaitum concipiatum spatium
BF N in sua filamenta per applicatas verticales PF, pl H. situ
linea BL, cujus applicata GL denotent gravitationes liquores
in altitudine BG seu PF, id eit cusus applicatae ex. gr. GL et ED
ortendant rationem in qua liquoris particula FC in protunditate
PF magis gravitet seu magii prematum ab incumbente ponderetica
ment. PFCp, quam aequalis particula Mm in profunditate PMipre
hitur ab incumbente pondere tilarenti spr. cum ergo LG de
240