# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/DE-611-HS-958803:0417
# Permalink to this reading: https://leibnizlegible.com/page/DE-611-HS-958803:0417?run=74
# Title: LBr. 57, 1 · Bernoulli, Joh.
# Folio 208r, page id DE-611-HS-958803:0417
# Scan: One image of two folio pages side by side, registered by the library under both labels (also fol. 203v); this page is its right half.
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=DE-611-HS-958803&page=417
# Source image: https://digitale-sammlungen.gwlb.de/content/DE-611-HS-958803/jpgs/default/00000417.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 42 lines, status machine
# Lines: 42 recognised, mean confidence 0.91
# 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.

ed quod ais problema esse plus quam determinatum
quoties quaeritur medium in quo radii in datam Lineas
non transeant; id velim denuo examines; fortasse
enim rem semper possibilem deprehendes. Nam
NAC
 in omni superficie, adeoque et plano assumi
possunt non tantum infinita ut in linea, sed
et infinities infinita. Si igitur varies medium
uno tantum modo. ita verbi gratia, ut varietas
solum assumatur secundum lineam ABCdE, et ut
tota BB, tola CC, etc. unam subeat legem variatio
nis seu sint ejusdem densitatis tunc fateor problema fore plusquam
necretert (_ BB verbi Gratia rectasit an scurva,
ta
determinatum. sed si rursus alia variatio concurrat secundum lineam p
seu ut variatio sit duarum dimensionum, ita ut quo quodlibet plani punctum
a quolibet densitate differat,  ut BL non tantum differat a puncto BM.
seu punctum
sed et a purcto CL. tunc possibile utique est variationem densitatis
in quovis puncto eam esse, ut ibi curva stranseat prout desideramus
linea radii
ausa  hoc problema: invenre lineam AMB antex
duo) puncta A et B quae ex omnibus curvis ejusdem
eagitudinis  brevissimo tempore pet curratur simplici
illa nethodo qua in brachystochiona sab soluta susi sumus
cractari non possit, h e nec debeat haec est, ponamue
etiam particulam quamvis ejusdem naturae, ea sit inde-
finite parva Lpx constans  ex duaibus rectis LM, MN
ut in methodo brachystochionae absolutae, patet rem
ferae plus esse plus quam deter minatam, punctum
e
rem aeque esse facilem in recta
decere
Nuspiam memini me se
appultu ad rectam et ad curvam interim suaserim pro curvu data, substitur
vi
altum e simileu
similiter positam ad assumtam, ut data est ad quaatam
n sit per spectissima, T quae in eo cosistitat
cum Tibimethodus inea
in parte feu s lex minium et in pardicula locum habeat, Tibi ipsi facillimum
vel maxim