# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/1041163592:0140
# Permalink to this reading: https://leibnizlegible.com/page/1041163592:0140?run=74
# Title: [Philosophiae Naturalis Principia Mathematica] Philosophiæ Naturalis Principia Mathematica (shelfmark Leibn. Marg. 166)
# Folio 106, page id 1041163592:0140
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=1041163592&page=140
# Source image: https://digitale-sammlungen.gwlb.de/content/1041163592/jpgs/default/00000140.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 40 lines, status machine
# Lines: 40 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.

206
PETTLOSODHTTHE NATDRALIS
DE MOrD Cas. 2. Si Figura illa R F B FIrperbOla eA, describatur ad Car-
dem diametrum principalem AB IIrperbola rectangula B L D:
ex quoniam arcx CSP, CBfP, SP fB TunC ad arcaS CSD,
CBF D, SD F B, lingulae ad singulas, in daca ratione alticudi-
num CF, CD; ec arca SF fB
proportionalis est tempori quo
COrDUS F morebIEur PEF aECUM
fB; CrIE etiam arCA SDF. B ci
dem cempori proportionalis.
Minuatur lacus rectum IIyper
bola R F B in infinicum ma-
nente latere trantverlo, ex coibit
arcus F B cum recta CB ec um-
bilicus Scum vertice B ee recta
SD cum recta B D. Proinde a
rea BD F B proportionalis crie
tempori quo corpus C recto
descensu describie lineam C B.
d. F. I.
Ca5. 3. FF Simili argUmenEO SI
Fisura RP B Parabola CA, de
eodem vertice principali B de.
scribatur alia Parabola BF D,
ouae semper maneat data interea
dum Parabola prior in CujuS PCrImMCETO COrDUS P MOVCEUF, dimi
nuto ex in nihilum redacto ejus latere recto, conveniat cum linca
CB; Het scomentum Parabolicum B D F B provortionale tempori
quo corpus illud P vel C descendet ad centrum S vel B. 9. F.. L.
PROPOSITIO XXXIII THEOREMA IX.
Positis jam inventis, dico quod corporis cadentis Velocitas in loco quo
vis C est ad velocitatem corporis centro B intervallo BC Circu-
lum describentis, in sub duplicata ratione quam AC, distantia cor-
poris a C irculi vel Fyperbolae rectanculae vertice ulteriore A, habet
ad Ficurae semidiametrum principalem = AB.
BisCCCtuT AB, communis utriusque Figura R F B, D F B dia
meter, in O; ec agatur recta PF quae tangat Liguram RP B in P, acque
etiam
EOEONOH