# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/1041163592:0059
# Permalink to this reading: https://leibnizlegible.com/page/1041163592:0059?run=74
# Title: [Philosophiae Naturalis Principia Mathematica] Philosophiæ Naturalis Principia Mathematica (shelfmark Leibn. Marg. 166)
# Folio 25, page id 1041163592:0059
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=1041163592&page=59
# Source image: https://digitale-sammlungen.gwlb.de/content/1041163592/jpgs/default/00000059.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 36 lines, status machine
# Lines: 36 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.

PAINOIPIA MIATHOMMLLCA.
L E MI M A II.
Si in Firura quavis AACE, rectis Aa, AF. Cs curva 2CF. com-
prehensa, inscribantur parallelorramma quotcunque AB, BC, C d,
dec. sub basibus AB, BC, CD, _C. aequalibus, ex lateribus
Bb, CC, Dd, RC. Firurae lateri A a pa.
rallelis contenta; e compleantur paral.
leloeramma aK bI, bLCm, CMdm, _c
Dein borum parallelorrammorum lati-
tudo minuatur, es numerus auceatur
in infinitum: dico quod ultime rationes,
quas habent ad se invicem Ficura in-
Scripta ARDLCMdD, circumscripta
AalbmendoE, es curvilinea AabCdE
sunt rationes aequalitatis.
Nam Figurae inseripex ex circumseripex differentia est summa pa-
rallelogrammorum RLB, L. m, Mn, Do, hoc CA (ob aequales om-
nium bascs) rectangulum sub unius basi Rb ec alcitudinum summa
Aa id est, rectangulum ABIa. Sed hoc rectangulum, co quod
lacitudo ejus AB in intinitum minuitur, fit minus quoris dato. Fr-
∞0 (per Lemma 1) Figura inscripra et circum seripta ec multo magis
Figura curvilinca intermedia tiune ulrimo aequales. Q. P. D.
L F MI M A III.
Faedem rationes ultimae sunt etiam rationes aequalitatis, ubi paral-
leloerammorum latitudines AB, BC, CD, XC. sunt inaequales,
e omnes minuuntur in insinitum.
Sic enim AF aequalis lacicudini maximae, ec compleatur paralle.
locrammum F Aaf. Hoc cric majus quam difterentia Figurae in-
seripeae ex Figurx circum scripex; at lacitudine Cua AF in infinicum
diminuta, minus het quam datum quodris rectangulum. 9. F. D.
Corol. I. Tlinc summa ultima parallelogrammorum cranescentium
coincidit omni ex parte cum Figura curvilinca.
Corol. 2. Ec multo magis Figura rectilinea, quae chordis eranel
CENEIUI
C. IB
PR1AVE.