# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/1041163592:0136
# Permalink to this reading: https://leibnizlegible.com/page/1041163592:0136?run=74
# Title: [Philosophiae Naturalis Principia Mathematica] Philosophiæ Naturalis Principia Mathematica (shelfmark Leibn. Marg. 166)
# Folio 102, page id 1041163592:0136
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=1041163592&page=136
# Source image: https://digitale-sammlungen.gwlb.de/content/1041163592/jpgs/default/00000136.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 42 lines, status machine
# Lines: 42 recognised, mean confidence 0.90
# 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.

1O2
PTIILOSOPMLA NAIORMLI
De Moro lionalis, id est, qui sic ad quatuor rectos, ut est tempus quo corpus
orronom delcripsit arcum Ap, ad tempus rerolutionis unius in Lllipfi. Sit
angulus iste NV. Tum capiatur ex angulus D ad angulum B, ut
est sinus iste ansuli A0  ad radium, ec angulus F. ad angulum
N - AO ∞ + D, ut est lonsitudo L ad lonsicudinem candem L
colinu ansuli O a diminutam, ubi angulus ilte recto minor est,
auctam ubi major. Postea capiatur tum angulus F ad anoulum B,
uE eAt sinus anguli AOO + F ad radium, tum angulus (+ 2d anou-
lum N = AO  =F + F uE est longitudo L ad longicudinem can-
dem colinu anguli AOO F P. diminutam ubi angulus iste recto mi-
nor est, auctam ubi major. Terria vice capiatur angulus FT ad an-
culum B, ue est sinus anculi AO G F F. F C ad radium; ex anou-
lus I ad angulum N - AO9 =F - C f II, ut CAt longitudo L ad
eandem longitudinem colnu anguli AO Q + P. + C diminutam,
ubi angulusistere-
eto minor est, auc-
tam ubi major. lE
Sic pergere licet in
infinitum. Deni-
que capiatur angu
lus AO9 aequalis
angulo AO_ = H
+ C + I F _C. C
ex colinu ejus O,
e ordinata p r.
cA ad linum ejus
gr ue Fllipleos axis minor ad azem majorem, habebitur corvoris
locus correctus p. Si quando angulus N - AO _ F D negacirus
eA, debet signum F ipsius F ubique mutari in -, ex signum - in f.
idem incellisendum est de signis iplorum C ec P, ubi anguli
N - AO O -F, + F, _NI = AO9 -F -C, + II negaciri prodeunt.
Conversie autem series infinica O + F + C + I + ecc. quam
celerrime, adeo uc rix unquam opus tuerie ulera prosredi quam
ad terminum secundum P. Fe fundatur calculus in hoc Theore
mate, quod arca  P S Sc uc differencia inter areum A et
rectam ab umbilico S in Radium O a perpendiculariter de
mictam.
Non distimili calculo conticitur Problema in FIyperbolo. Sit
ejus Centrum O, Vercex 4. Ombilicus Sec Asymproros O H. C08.
nOlcatuE