# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/1041163592:0409
# Permalink to this reading: https://leibnizlegible.com/page/1041163592:0409?run=74
# Title: [Philosophiae Naturalis Principia Mathematica] Philosophiæ Naturalis Principia Mathematica (shelfmark Leibn. Marg. 166)
# Folio 375, page id 1041163592:0409
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=1041163592&page=409
# Source image: https://digitale-sammlungen.gwlb.de/content/1041163592/jpgs/default/00000409.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 43 lines, status machine
# Lines: 43 recognised, mean confidence 0.91
# 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.

IIIII
RENCTDTA MATHEMATTCA.
ROPOSITIO XII.
THEOREMA XIII
Planetae moventur in Fllipsibus umbilicum habentibus in centro
Solis,  radiis ad centrum illud ductis areas describunt
temporibus proportionales.
Dispurarimus supra de his moribus ex Phxnomenis. Jam cog-
nicis motuum principiis, ex his colligimus motus calettes a pri-
Ori. Ouoniam pondera Planetarum in Solem unt reciproce uE
quadrara distantiarum a centro Solis; (I Sol quiesceret e PlanCEX
reliqui non agerene in se mutuo, Forent orbes corum Ellipticis
Solem in umbilico communi habentes, et areae describerentur tem-
Poribus proportionales (per PFOP. L. _ XF, de CorOl. L. PrOP.
ZITT LIb. I.) Actiones autem Planccarum in se mutuo perexiouae
TUInE (BE POssinE contemni) se mocus Planccarum in FIipsibuS
circa Solem mobilem minus perturbant (per PFOP. LXVF. L ib l.)
quam si motus isti circa Solem quiclcentem peragerentur.
Actio quidem Poris in Sacurnum non est omnino concemmenda.
Nam graritas in forem est ad gravitarem in Solem (paribus di-
Aantiis) ut 1 ad 2033; adeoque in conjunctione joris de Saturnis
quoniam distantia Saturni a Pore est ad distantiam Sacurni a Sole
fere uc q ad on erit gravitas Saturni in fovem ad graritarem Sa-
turni in Solem uE 8F 2d 16X 1033 TCu F 2d 204 Circiter. LE
hinc oritur percurbatio orbis Sacurni in singulis Planetxe hujus
cum Jore conjunctionibus adeo sensibilis ue ad candem AAronomi
hareanE. Pro vario situ Plancex in his conjunctionibus, FCCCN-
tricitas ejus nunc augetur nunc diminuitur, Aphelium nunC prO-
moretur nunc Forte recrahitur, ex medius motus per rices accele.
ratur ec recardatur. Frror eamen omnis in motu ejus circum So.
lem a tanta ri oriundus (praeterquam in mocu medio) evitari ferc
potest constituendo umbilicum inferiorem Orbis ejus in communi
centro graricaris soris ex Solis (per Prop. L. XVII. Lib. l.) ee prop-
cerea ubi maximus est, rix superat minura duo prima. LE CrrOr
maxImUS in motu medio vix luperat minuta duo prima annuacim.
In conjunctione autem foris ec Saturni gravitates acceleratrices
Solis in Saturnum, foris in Sacurnum ee foris in Solem lunc fere
Uc 16, 82 _ 10X81 X 2411 feu 124986, adeoque difterencia gravi-
cacum solis in Saturnum ee foris in Socurnum est ad gravicacem
Toris
F. R
TERZ1V5
NIsA.LL MIIHIIIABIII