# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/1041163592:0303
# Permalink to this reading: https://leibnizlegible.com/page/1041163592:0303?run=74
# Title: [Philosophiae Naturalis Principia Mathematica] Philosophiæ Naturalis Principia Mathematica (shelfmark Leibn. Marg. 166)
# Folio 269, page id 1041163592:0303
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=1041163592&page=303
# Source image: https://digitale-sammlungen.gwlb.de/content/1041163592/jpgs/default/00000303.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 45 lines, status machine
# Lines: 45 recognised, mean confidence 0.88
# 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.

PRTNOTPTA MAEETEMAETC A.
cur jam distantix quaelibet, puta S A, SD, SF in progrestioneMU. LIDEn
lica, e disterentix Aa =D de D d = F f erune aequales; e PFOPECE. SECoND.
ea difterentiis hisce proportionales arex thla X In Z aequales CrUNE
inter se, _ denstates S+ Sa, 52, id cA, AFE, D L FN, conci-
nue proporcionales. D. L. D.
Corob. Hlinc A dentur Fluidi densicates dux quevis, puta AII
Ee CR, dabitur are Fhkr harum disterentixe + re respondens; et
inde invenietur densitas Si N in alcitudine quacunque SF, sumen-
do aream thn Z ad aream illam datam shkwe ut est disterentia
Aa - Ei fad difterentiam Aa = C c.
Scholium.
Simili aroumentatione probari porest, quod si Graritas partieu-
larum Fluidi diminuatur in criplicaca racione distanciarum a CCNErO
ec quadratorum distantiarum S , SB, SC, Scc. reciproca (nCm-
De dAcub: S Acub. SAcub.
SA
dB9
Sc q Cumantur in prosressione Arichme
tica; densITateS AFI, BL CK, ec. crunt in progrestione Geome
trica. FC E gravitas diminuatur in quadruplicata racione distan-
tiarum, de cuborum distantiarum reciproca (puca
5 Agq
SCcub
SAg9 SAgq
SACub SBCub.
ecc.) Tumantur in progrestione Arithmerica; denlitates
AH BB CK, _c. erune in progrestione Gcometrica. Ex sic in
intinicum. RursuS S graritas particularum Fluidi in omnibus di-
sanciis eadem sc, ec distantixe sine in progrectione Arichmetica
densitates crune in progressione Geometrica, vri Vir CI. Lamundus
Flalleius invenie. Si graricas siE ut distantia, ec quadrata distantia-
rum sinc in progrectione Arichmetica, densitaTeS crunt in progre
sione Ceometrica. FE sic in infinitum. Flxec ica se habent ubi Fluidi
comprestione condenlati densitas est ut vis compressioniss vel, quod
perinde est, sparium a Fluido. occupatum reciproce ut hrC Vis.
Finsi portunt alix condenlationis Leses, uc quod cutus ris com
primeneis sE ue quadraco. guadratum densitatis, scu criplicata ra-
eio Vis aequalis quactruplicatae rationi densitatis. Duo in casu, ( GFa-
vitas est reciproce uc quadratum distantix a cenero, densitas crie
reciproce ue cubus distantix. Fingatur quod cubus ris compri-
MenEiS SIE UE quadrato cubus densitatis, _ Si gravitas est reciproce
ux quadracum distancireo densiras exir reciproce in sesquiplicata ta
tione
aC