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# Title: [Philosophiae Naturalis Principia Mathematica] Philosophiæ Naturalis Principia Mathematica (shelfmark Leibn. Marg. 166)
# Folio 73, page id 1041163592:0107
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=1041163592&page=107
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# 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.
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# After the first blank line: the recognised lines in reading order, one per line.

1
Nam in recta MN decur punctum Les ec ubi punctum mobile exiuvo
M incidic in immotum N, incidac punctum mobile D in immo-
cum P. JunscCNP, BNI,
P, BF, ex a puncto
P asC rectas FZ, PR
Occurrentes ipss B D.
CD in F _ R, e Fa-
cientes angulum B F Y
aequalem angulo dato
B N M. ec angulum
CP R aequalem angu-
gulo datoCNM. Cur
ergo (ex HIrpothesi
aequales sine anguli
MBD, NBF, ut dc
anguli MCD, NC P
auter communes NB D
_ NC D, ee rectabune
aequales NBMI _ PBT,
NCMAF CR: adeoque criangula NB M, P BZ Similia UnE, UE
ec triangula NOM, FCR. OUare PT eA ad NM uE P B ad
NVB, _ F R ad NNNE FC ad NC. Sune autem puncta B, C, NV, Y
immobilia. Rroo F T et F R datam habent racionem ad NMI, PFO-
indeque datam rationem inter (C; atque adeo, peF L CMMa XX)
punctum D (perpetuus rectarum mobilium BY et C R concurtus)
contingit sectionem Conicam, per puncta B, C, P transcuntem.
Q. F. D.
Ec contra, si punctum mobile D contingat sectionem Conicam
transcuntem per data puncta B, C, A, e Sc angulus D B M TemPCF
aequalis angulo dato ABC, ex angulus DCM Temper aequalis ansu-
lodato ACB, et ubi punctum D incidit successire in duo quaeris se-
ctionis puncta immobiliap, P, punctum mobile M incidat successive
in puncta duo immobilia n, NV: per cadem n, N agatur R oct a n N,
e haec erit Locus perpetuus puncti illius mobilis M. Nam, A feri
Potest, versetur punctum M in linca aliqua Curra. Tanset ergo
punctum D sectionem Conicam per puncta quinque B, C A, p, F.
cranscuntem, ubi punctum M perpetuo tangir lineam Curvam. Scd
ec ex jam demonstratis tanset etiam punctum D sectionem Coni-
Cam per eadem quinque puncta B, C, A, P, P cranscuntem, ubi pun-
ctum
RINCTPTA MATETEMATICA.