# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/1041163592:0171
# Permalink to this reading: https://leibnizlegible.com/page/1041163592:0171?run=74
# Title: [Philosophiae Naturalis Principia Mathematica] Philosophiæ Naturalis Principia Mathematica (shelfmark Leibn. Marg. 166)
# Folio 137, page id 1041163592:0171
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=1041163592&page=171
# Source image: https://digitale-sammlungen.gwlb.de/content/1041163592/jpgs/default/00000171.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 38 lines, status machine
# Lines: 38 recognised, mean confidence 0.89
# 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.

PRTNCIPLA MATHEMATICA.
is
id est, rario mutationum momentanearum curvae AP, rectxe LIbe
CF, arcus circularis BF, ac rectae VP, eadem erit quae linca-
rum PV, PF. FC, PY respectire. Cum autem V. F ad C F et
II ad CV perpendiculares sunc, angulique AIVO, VCF prop.
terea aequales; ex angulus VHIO (ob angulos quadrilateri YIV F F
ad V ec P rectos) angulo CF. P aequalis eAt, limilia CruINE FrI
angula VIIO, CF. P; _ inde ACE UE F. P ad C F. ica NIC ad YIB
seu TYP ec ita R Y ad R P, de composire vel divisim ut CB ad
CF Ita P Y ad P K, e duplicatis consequentibus uc C B ad 2 C F
ita P I ad P V, atque ita adco P g adt P m. F. s isitur decremen-
cum lincae V P, id CA, incrementum lincae BV = V P ad incremen-
tum lincae currae AF in data ratione C B ad 2 CF, _E PTOP.
cerea (per Corol. Lem. IV.) lonsitudines BV - V P de AF, in-
crementis illis genitae, sunt in eadem ratione. Scd, existence BV r2-
dio, eAtV P co sinus anguli BV P Pcu = BF. P, adcoque BV -V Y
sinus versus ejusdem anguli; e propterea in hac Rota, cujus radius
CA = BV, Crit BV =V P duplus linus versus arcus = B F. PrgO
AF cA ad duplum sinum versum arcus = BP Ut 2C F. ad CB.
2. F. D.
Lineam autem AP in Proxostione priore Ccloidem extra
Globum, alteram in posteriore Cycloidem intra Clobum distincti.
onis gracia nominabius.
Corol. 2. Flinc A describatur Crclois inceora ASP _E BISCCCTUE
ea in S, erit longieudo partis P S’ad lonsicudinem V P (quae du-
plus est sinus anguli VB P, existente P B radiO) uE 2C F ad C B,
acque adeo in ratione data.
Corol. 2. Uc longitudo semiperimeeri Crcloidis AS equabitur
lineae rectae quae eA ad ROI_ diametrum BV, UT 2 C F. 2d CB.
eROPOSITIOL. PROBLEMA ZZXIII.
Facere ut Corpus pendulum oscilletur in Cycloide data.
Intra Globum QVS, cenerO C descriprum, detur Cyclois QRS
bilecta in R ex punctis luis extremis  e S superticiei Clobi hinc
indC OCCUErENS. RGatuF C R bisecanS arcum QS in O, ec produca
cux ea 2d A, uC sIC C A 2d C O uc C0 ad C R. Centro C in
terrallo
P et hev