# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/1041163592:0307
# Permalink to this reading: https://leibnizlegible.com/page/1041163592:0307?run=74
# Title: [Philosophiae Naturalis Principia Mathematica] Philosophiæ Naturalis Principia Mathematica (shelfmark Leibn. Marg. 166)
# Folio 273, page id 1041163592:0307
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=1041163592&page=307
# Source image: https://digitale-sammlungen.gwlb.de/content/1041163592/jpgs/default/00000307.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 40 lines, status machine
# Lines: 40 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.

PRINCIPTA MATHEMAETCA.
297
Corol. 4. Unde cum quadrata temporum, caeteris paribus, sInE UE LEVEn
longitudines pendulorum; si de tempora et quantitates materix X- SEcvnDOS.
qualia sune, pondera crune ue longicudines pendulorum.
Corol. 5. FF univerlaliter, quancitas materix pendula est ut pon-
dus e quadratum temporis directe, ex longitudo penduli inverle.
Corol. 6. Sed ec in Medio non resiltente quantitas materiae pen.
dulxe est ut pondus comparatirum ex quadeacum cemporis directe
et longitudo penduli inverse. Nam pondus comparatirum est vis
motrix corporis in Medio quoris graris ut supra explicui; adcoque
idem praestat in tali Medio non relicente acque pondus absolutum
in vacuo.
Corol. 7. EE hinc liquet ratio cum comparandi corpora inter (c,
quoad quantitatem materix in sinsulis; cum comparandi pondera
ejusdem corporis in diversis locis, ad cognoscendam variationem
sravitacis. Factis aurem experimentis quam accuratistimis inveni
Cemper quanticatem materixe in corporibus lingulis corum ponderi
proportionalem esc.
PROPOSITIO ZEV. TTTEOREMA XZ:
Corpora Punependula quibus, in Medio quovis, resistitur in ratione
momentorum temporis, es corpora Funependula quae in ejusdem
gravitatis specificae Medio non resistente moventur, oscillatio-
nes in Cyeloide eodem tempore perasunt,  arcuum partes pro-
portionales simul describunt.
Sit AB Creloidis
aECUS, Quem corpuS
Dcempore quovis in
Medio non relistente
oscillando describit.
Bisccetur idem in C3
ita uc C CC infimum
ejuspunctum; ex erit
vis acceleratrix qua
Corpus ursetur in lo-
co quoris D vel a vel
P ut lonsitudo arcus
CD vel c: d vel CF. Exponatur vis illa per custe drcum; de
cum relistentia sic uc moniencum cemporiss adeoque decur, exporu
CUIT