# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/1041163592:0145
# Permalink to this reading: https://leibnizlegible.com/page/1041163592:0145?run=74
# Title: [Philosophiae Naturalis Principia Mathematica] Philosophiæ Naturalis Principia Mathematica (shelfmark Leibn. Marg. 166)
# Folio 111, page id 1041163592:0145
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=1041163592&page=145
# Source image: https://digitale-sammlungen.gwlb.de/content/1041163592/jpgs/default/00000145.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 28 lines, status machine
# Lines: 28 recognised, mean confidence 0.92
# 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.

PRINOIPLA MATHEMATICA.
Dein junctis SF, SD, hane segmentis SF IS, SF. DS, sec-
TOrCS TTSR, HTSK aequales, eE Per PFOD. XXXV, corpuS C deseri PRIb
bec spatium C C eodem Tempore quo corpus  delcribere P0.
cest areum RR. R. F. F.
PROPOSITIO ZZXVIII. ZHEOREMA XII.
Posito quo d Vis centripeta proportionalis sit aliitudini seu distantiae lo-
corum a centro, dico quod cadentium Tempora, Velocitates e Spa
ria descripta sunt arcubus, arcuumque sinibus rectis e sinibus
versis respective proporcionalia.
Cadat corpus de loco quoris A secun-
dum rectam AS; ex centro ririum S, in-
cerrallo AS, delcribatur Circuli quadrans
AE, ACque C D Sinus rectus arcus cujus-
vis AD; _ COrpUS A, PenpOre AD, Ca-
dendo describet Spatium AC, inque l0c0
C acquiret Velocitatem CD
Demonstratur eodem modo ex PrOPOI-
tione X, quo PFODOsITIO ZXXII ex PrODO
sitione XI demonstrata fuit.
Corol. 2. Tlinc aequalia sune Pempora quibus corpus unum de loco-
A cadendo pervenit ad centrum S, ee corpus aliud revolvendo de-
seribit arcum quadrantalem AD F.
Corol. 2. Proinde aqualia sune Fempora omnia quibus corpora de
locis quibulris ad ulque centrum cadune. Llam revolventium tem-
Pora omnia periodica (per Corol. 3. PrOD. TV.) aequantur.
PROPO.
E. L B. E. K