# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/DE-611-HS-958803:0167
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# Title: LBr. 57, 1 · Bernoulli, Joh.
# Folio 83r, page id DE-611-HS-958803:0167
# Scan: One image of two folio pages side by side, registered by the library under both labels (also fol. 85v); this page is its right half.
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=DE-611-HS-958803&page=167
# Source image: https://digitale-sammlungen.gwlb.de/content/DE-611-HS-958803/jpgs/default/00000167.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 32 lines, status machine
# Lines: 32 recognised, mean confidence 0.96
# 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.

invenire Lineam Jachystoptotam
datis, in plano verticali duobus punctis
AB AMB AB invenire lineam AMB, per quam mobile M
a puncto M moveri incipiens  propria gravitate descendens,
perveniat ad punctum B tempore omnium possibilium brevissimo
invenite lileam Tueches stopto
inde a quiete
si pave M descendat in recta inclinata AB erit tempus quo percurrit
,AB, ad tempus quo percurrit Ac perpendicularem usque adhorizantalem
Rursus si ponamus CB esse duplam ipsius AC, et grave ubi descensu
CB, ut AB ad AC ut constat
pervenit a ad C pergere in horijonte concepto impetu, ac tendere motur
equabili versus B, percurret CB tauto tempore, quanto AC; sin CB sit aqualis
Ae percurret dimidio, et in universum tempus quo percurritur CB ert ad
tempus quo percurritur AC, ut CB ad bis AC a Renepus quo per
venitere  in B bin ACeB Tempus quo percurritur AC  vel quo
in honizonte percuritur bis AC sit t, erit tempus per cB ad + ut CB ad bis AC
seu tempus per CB aequ. t. CB: bis AC. Ergo tempi pervenitur ex A in B
per ACB erit t + + (CB: bis AC) seu t, bisAC+ CB,: bis AC. sed tempus
quo pervenitur recta  ex A in B per AB, est FAB: AC. quorum hoc e potest
esse majus quam illud. Nempe _ AB major quam:  (bi AC) + CB 2 2AC + CB,: 2
seu ACE+ CB maj. quam 4AC + 4AC. CB L CB: 4 et demtis communibus
cB majo 4AC. CB + CB,. + seu 4CB maje +AC + CB seu 3CBmaj. 4AC itaque
per AC B AC B brevius est quam tempus seu 4AC2 + 4CB maj. 4AC + 4AC + CB2
sei 3CB maj. 4AC Unde, si CB major quam Z AC brevius est tempus per ACB
quam per AB; siu minor sit longius est denique si CB = 3AC) seu si Triungule
ABC sit pythagoricum, quod vocant, ubi latera AC, CB, AB, sint, ut 3, 4,5, eodem
tempore pervenitue ex A ad B per ACB, et per AB. Ubi tamen in prari
concipiendum est angulum C nonnihul restundari se constare ex partiuncula
curvae cujus tangentes sint rectae AC, et CB.  sine res lxiole vel impedimento
motus  corporis gravis ex Aper C ad CB procedat. sed portiuncula sufficit
quantunvis parva, quod tamen notabiliter Calculum non mutat.