# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/1041163592:0387
# Permalink to this reading: https://leibnizlegible.com/page/1041163592:0387?run=74
# Title: [Philosophiae Naturalis Principia Mathematica] Philosophiæ Naturalis Principia Mathematica (shelfmark Leibn. Marg. 166)
# Folio 353, page id 1041163592:0387
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=1041163592&page=387
# Source image: https://digitale-sammlungen.gwlb.de/content/1041163592/jpgs/default/00000387.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 42 lines, status machine
# Lines: 42 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.

1
PRINCTPTA MATHEMATICA.
Vortices explicari postint. Nam Phaenomenon est, quod Planeta-
L. TB B. R
rum circa Jorem revolventium tempora periodica lune in ratione SEcvWDOS.
Tesquiplicata distantiarum a centro foris; et eadem Regula obti-
nec in Planetis qui circa Solem revolvuntur. Obtinene autem hX
Regulae in Planctis verisque quam accurarissime, quatenus obser-
rationes Astronomicae hactenus prodidere. Ideoque si Planetse
illi a Vorricibus circa Torem ex Solem revolventibus deferanEUT,
debebunt etiam hi Vorrices cadem lege revolvi. Verum tempora
Periodica partium Vorricis prodierune in ratione duplicata distan-
ciarum a centro motus: neque potest racio illa diminui et ad ra-
tionem sesquiplicatam reduei, nisi vel materia Vorticis eo Auidior
sc quo lonsius distat a cenero, vel relistentia, quae oritur ex de-
tectu lubricicaris parcium Auidi, ex aucta velocitate qua partes
Ruidi separantur ab invicem, auscatur in majori ratione quam ca
est in qua relocicas ausetur. Juorum tamen neuerum rationi
consentaneum videtur. Parres crastiores ec minus Auidae (nili sra-
ves sinc in cenerum) circumterentiam petent; ex verilimile eA
quod, etiamsi Demonstrationum gratia Arpochelin calem inicio
Sectionis hujus propoluerim ut Relictentia relocitati proportiona-
lis esset, tamen Relictentia in minori sic ratione quam ca velocita-
eis est. Duo concesso, tempora periodica partium Vorricis crune
in majori quam duplicata ratione distantiarum ab ipsIuS CCnErO.
Duod s Vorrices (uri aliquorum eAt opinio) celerius moveantur
Prope centrum, dein cardius ulque ad certum limitem, cum denuo
celerius juxta circumferentiam; certe nec ratio selquiplicata neque
alia quaeris certa ac determinara obtinere porest. Viderint itaque
Philo(ophi quo pacto Phaenomenon illud rationis Cc squiplicatx Per
Porrices explicari poMit.
PROPOSITIOLMI. TTTEOREMA XLI.
Corpora quae in Vortice delata in orbem redeunt, ejusdem sunt den-
sicatis cum rortice, e eadem lere cum ipsius partibus (quoad
velocitatem e cursus determinationem) moventur.
Nam Si Vorticis pars aliqua exigua, cujus particulxe seu puncta
physica datum serrant sicum inter le, congelari sUPPONaEUE: haeC
quoniam neque quoad densicarem cuam, neque quoad vim insitam
auc figuram suam mucatur, morebitur eadem legc ac prius: de
COntra,
11I
NTIPTSIIHHIEMHIINIHHAMSIMAIHHIIIMIIMIIMMMINMINAIHMBIIIIMMHII