# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/00068164:0221
# Permalink to this reading: https://leibnizlegible.com/page/00068164:0221?run=74
# Title: Leibniz-Handschriften zur Mathematik LH 35, 10, 11
# Folio 111r, page id 00068164:0221
# Scan: One image of two folio pages side by side, registered by the library under both labels (also fol. 110v); this page is its right half.
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=00068164&page=221
# Source image: https://digitale-sammlungen.gwlb.de/content/00068164/jpgs/default/00000221.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 88 lines, status machine
# Lines: 88 recognised, mean confidence 0.85
# 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.

tangente ipsius AM, vel in MK Hngente ipsius NM
si mobile feratur in inea
quacunque AM vel NM
vacunque directio ejus erit,
 ut in AY nu
Am tangente CeeM
Unde sequitur si motus
in linea
junde sequiur
y se mole mot
ejus sit compositus ex circulatione circa centr
et descensorio descensu, versus centrum
fore
erit velocitaten circulati descensus ad
velocitatem circulationis  (posita ut
7
ad velocitatem descensus, ut recta extangente
ducta
ux radio nM normaliter occurrens
Mo
ate
normalem hanc
per maelediptem
radii partem. Nam circulationi
motis
et  lineam
directio est in operpendiculari ad radium nempe
NM ost mta
in MH tangente circuli e centro, C radio CdM descr
deversus contrum si
et directio descensus cest in recta M MO
sit ergo directio. Cum ergo directio ei
si ergo directio Et proinde dinectio velocitatis
et circulationis et descensus fa
invicem angulum rectum.
cum
Ca ergo direct
ex. utraque erva composita repraesentetur,
C
agentem
o
per on
portionem tangentis ab ut
livet assumtam
na directione diculationes
et velocitates circulationisres descensus
a
md. sD
componegteta
repraesebtabuntur per, rebta latera anguli
e
tenusa est MT,  ex quibus unumnd utique
quibus unum cadat in MO, ac proinde habebitur
recti, cujus
a censum
utrumque demissa s D normali ex T in OM
Ex His jam poterimus Geometiice demonstrare
stratione
positis
in circulatione Harmonica sectorum
unsesteri AN NM A
sit enim curvae 
se
t
4
arcas foreut tempora
AMM circum scriptum polysgonum quantilibet punr
(1IL 2L3La
laterum quantum sufficit, ut differentia ejus ab sipso
sciliee
curvae sectore sit minori data, et differentia penipheriae
qubit
in lateribus potygom describetur linca a curva
parne iia ideo
quantillum libet differens. Ics Ex punctis (L2 et
lagantur normales LN in d issas B, diL ek. et
ipsa ponendo aequalibus temporibus percurri BIL, 1C etc eti
cd
et derectionem BIL vel iL 2L comprni BIN, et N cum
dircetiones in lateribus,  ut it 2L, sint compositae ex directionibus
ut IL 1N) et e. NN2L, _ ipsae entem directiones et ideo temporibus
+ taque si per
eaudem reprae–
sentetur et
v
locitas directio
compositae
4