# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/1041163592:0208
# Permalink to this reading: https://leibnizlegible.com/page/1041163592:0208?run=74
# Title: [Philosophiae Naturalis Principia Mathematica] Philosophiæ Naturalis Principia Mathematica (shelfmark Leibn. Marg. 166)
# Folio 174, page id 1041163592:0208
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=1041163592&page=208
# Source image: https://digitale-sammlungen.gwlb.de/content/1041163592/jpgs/default/00000208.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 33 lines, status machine
# Lines: 33 recognised, mean confidence 0.82
# 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.

174
PHITLOSOPMILLE NATDRALIS
DEMod aqualitatis. Aecractiones igitur, in contrarias partes aequalicer fac-
CORPORDM EX. Se mutuo destruune. EE Simili argumenco, actractiones omnes
per tocam Sphaericam superticiem a contrariis attractionibus de-
Aruuntur. Proinde corpus P nullam in partem his actractionibus
impellitur. Q. F. D.
PROPOSITIO LXXI.
THEOREMA XXXI.
Ti(dem positis, dico quod corpusculum extra Sphaericam superficiem
constitutum attrabitur ad centrum Sphaerae, vi reciproce propor-
tionali quadrato distantiae suae ab eodem centro.
dint laB. aded aguales ce iapelcles spuaenica, centis
Si s, diametris AB, ab descripeae, ec P, p corpuscula sita exerin-
ecus in diametris illis productis.
Aganeur a corpusculis linex
PFTK, FTL. phB pE aCuS a Crcuns maximis AIIB,
miciantur perpenencula 5, 5a: da, se c1 13 guorcu
ahb, aequales arcus XTK, BK e YL, it: EF 2d cas de-
SD, Sa (CCenE F L p III L _ Y. DCMEICAMCO CCaM a Came.
rros perpendicula I9, ig. Pranelcane anguli D PF, dpe: &
(0b aequales DS _ a5, L8 a 153) a TF, FF _ pes p)
tio ulemuas angulis illis D L ap limul crancicentibus, est x
ec lincolae DF, af pro aguandud abeatur; quippe quarum ra-
qualitaris. Flis itaque constitutis, crit P Y ad P F ut RI ad D F.
_ pf ad p2 ut as ret L aur a esHOL LRPfad F FiXp
aicum ant Curtus P 12c10l2a add a ps aa pr ut s0
ve) dF 2di9; ex ex aequo F (Xp 5 ad FSX pi uE L  dl 19. L
AE R Y ad r i, hoc est (per Corol. 3. LCm. VTE) uE areuS YH ac
conjuncti racebus L L gumnks x aquad. X P F X
d
uc lLLXLd ad ihXig; hoc elt, ut lup elculatio quam
icu