# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/1041163592:0481
# Permalink to this reading: https://leibnizlegible.com/page/1041163592:0481?run=74
# Title: [Philosophiae Naturalis Principia Mathematica] Philosophiæ Naturalis Principia Mathematica (shelfmark Leibn. Marg. 166)
# Folio 447, page id 1041163592:0481
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=1041163592&page=481
# Source image: https://digitale-sammlungen.gwlb.de/content/1041163592/jpgs/default/00000481.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 44 lines, status machine
# Lines: 44 recognised, mean confidence 0.83
# 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.

PRINCIPTA MATHEMATTCA.
447
intervalla quacerna divisas c, 20, _c. _ sic deinceps; id CAt, IFa LIBEN
UE SIC 3 =
2a
3 2C =
2
3
X
3 36
C- DP
F
 dc. dein
3 3c - 3b = 4
KMI. dec. Postea d:
=_c. Inrentis disserentiis, dic ATI = a, -YIS = p,
P in -15 = g, g in + SR = r, r in + SF. = 5, 5 in + SM = t;
pergendo scilicet ad ulque perpendiculum penultimum MF, ec erit
ordinacim applicata RS = a + bp + c9 + dx + es + ft, ecc.
Corol. Tlinc arex curvarum omnium invenri postunt quampro-
xime. Nam Ei currae cujueris quadrandae inveniantur puncta ali-
quoc, ee Parabola per eadem duei intelligatur: erit arca P’arabola
hujus eadem quam proxime cum arca curra illius quadrandae.
Pocest autem P’arabola, per Mechodos nocissimas, lemper quadrari
Creometrice.
L F. MI M A VI.
Ea observaris aliquot locis Cometae invenire locum ejus ad
tempus quodvis intermedium datum.
DCTIOMeNE ETY, YK, KL, F M cempora inter observatiOnCSS
(in Fis. praeced.) II1, IB, KC, L. D, MF. obserratas quinque
Ponsitudines Comctx, LIS tempus dacum inter obserrationem pri-
mam ex lonsicudinem guaelitam. EE E Der puncta , B, C, D, P.
duci intelligatur, curra regularis ABCDF; et per Temma Cupe-
rius inveniatur ejus ordinatim applicata RS, erit RS longitudo
Quae(Ita.
Eadem methodo ex obserratis quinque lacicudinibus invenitur
laticudo ad tempus datum.
Si lonsitudinum obserratarum parvae sinc ditterentia, puta gra-
duum tancum 4 vel 5; Suffecerine obserrationes tres vel quatuor
ad inveniendam lonsitudinem ec lacicudinem novam. Sin majores
uinc disterentix, puca graduum 10 vel 20, debebune obserrationes
quinque adhiberi.
Tensto
I. F. MM A