# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/DE-611-HS-958803:0636
# Permalink to this reading: https://leibnizlegible.com/page/DE-611-HS-958803:0636?run=74
# Title: LBr. 57, 1 · Bernoulli, Joh.
# Folio 317v, page id DE-611-HS-958803:0636
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=DE-611-HS-958803&page=636
# Source image: https://digitale-sammlungen.gwlb.de/content/DE-611-HS-958803/jpgs/default/00000636.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 36 lines, status machine
# Lines: 36 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.

quoque compenclium nobis subministraret investivancti dicto
citius tempus descensus per quamcunq. curvam ad tempus
per altituclinem ejus venticalem ut ipsa curva ac ipsam
altitudinem.
Ex dictis liquet quanto consultius fecisset nndam ane,
vasse propositionem nobilissimi hujus inventi, et Lectorem
Temisisse ad demonstrationem Htuvenianam, quam suam nobis
obtrusisse sophistieam. Quod si vero Htuoeniana licet levitima
sect ob multarum propositionum farravinem et perplexitatem
non arrisit, rauclo propositum succinetiorem tractendi, modo
dradidios et oenuinam. Qua in re cum in scopo multum aberra
rerit; hic edo vices ejus supplebo demonstraturus brevissime
simul ac petspicue quod dn deloide cujus axis ad perpen.
diculum ereetus est, vertice deorsum spectante tempora.
descensus quibus mobile a quocunque in ea puncto dimissum
ad punctum imum vertiois perrenit, sunt inter: se aqualia
Oit scio: A. Cyclois FDC, enjus axis Atdd, Circulus
Generator ABD divo tempus per quamvis portionem GMD fore
aequale tempori per inteoram Semicycloidem SeD, Concipia
tur DG dirisa in partes indefinite parvas Mm ut et Dsi in
alias numero aequales Ee; unde erit partium curra in Dsi act
partium curram in DG, ut ipsa Dsi adt DG. Assumantur jam
ex illis partibus homolova Mm, Ce id est tales quae secant Ds;
D9 proportionaliter in E, M, ducanturque applicata es, M
item DB, DO. DL. Eroniam iortur per hypoth. Ds DC, et BG, D.M
sunt proportionales, Crodeiam eorum semisses qua por natu,
ram Cycloidis sunt A, DB et DL, DO, harumqu quadlvata sunt
proportionalia, id est DAg. DBg.  A, Ds):: D L9 ∞Oq. CDH
DN) dividendo Add, DG:: G1NDNV. ideoque ADq ANq (oeuper
naturam orarium descendentium velocitas in E ad velocitatem in MM)
: Sd Sq: D N:q. DB, BO: DC; OM: (per hyp.) Ec. Mm, quoniam
itaque relocitas in C est ad relocitatem in M, ut Cc act Mm, paret
quod tempus per ce sit aequale tempori per Mm ic quod de omni,
bus aliis portionibus homoloois demonstrabur, un de tempus per
Omnes Cc id est per D erit aequale tempori pet omnes Mm
id est pet DG; eroo descensus per Bs et D8 sunt Jsochroni. 2. 6. B.