# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/1040780814:0066
# Permalink to this reading: https://leibnizlegible.com/page/1040780814:0066?run=74
# Title: [Astronomiae Physicae & Geometricae Elementa] Astronomiæ Physicæ & Geometricæ Elementa (shelfmark Leibn. Marg. 124)
# Folio 48, page id 1040780814:0066
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=1040780814&page=66
# Source image: https://digitale-sammlungen.gwlb.de/content/1040780814/jpgs/default/00000066.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 60 lines, status machine
# Lines: 60 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.

ASTRONOMLA PATSICE
eo ad MoteB, 1C216
+.8
tione req ad ccg. Ouoniam isitut Lacio Ipsius L. = PR ad BBgcom
ponitur ex rationibus L X BR ad L PC
ad B0g, B0g ad BXG, eBXg au b DG; componitur etiam ex rati
onibus hisce respectire xqualibus; nimiru ex rationibus a c’ac
PC, L adt Mo, oxq ad 1C9.
et 2C9 ad cl, alleoque
aequalis crit ralIOTL ACLLL
PCg ad PCRMOKCCG: V
(Der Prop. XIII. Ldd. l. C d.
AC+Y = 26C9. Cb1BC
hoc illius Loco, Ct Tacte
L =BR ad BD4 xqualis rati
OniZGCGX P C G adl P CXHO
xCCq; hoc elt, rationt 2PC
ad Mo: Atqui (in calupia
senei, cum punctum B cst
ips e proximum) punctum
Ominime distat d P puncto.
hoc eAt, Mo aquatur 2 P c; _ iritur, in hoc catu, L = BR aequatur
BDg. Ouoniam erso, in FlipE, BDg = L - BR, exit 3 Bq uBDq
SFGKL. XBR
BR
=) SeqL L: Huic erso Solido Vis centripeta est reci.
proce proportionalis; e L est recta constans e invariata. Froo
Vis centripeta ad P. Iiplis umbilicum tendentis, (qua corpus à cursu
rectilinco perpetuo retractum in figura iltius perimetro detinetur,
cumque rerolrendo deseribit,) ea es Lex, ut sic Ouadrato distantix
loci p a centro s reciproce proportionalis. Quod erat inveniendum.
CiOROLLARTUM I.
Si Fllipto socuo s, ad Guem Vistendut, una cum vertice proximo
r mancat; alter vero F, ad hunc appropinquando, tandem cum illo
coincidat: Corpus e, eodem modo quo prius in perimetro FIlip(IS,
nunc in Curculi perimetro derinebitur à
Vi centripeta ad S tendente, e eddem
qua prius lesc ursente. Et Sicut Circu-
Jus potest à corpore describi, urgente Vi
qualibet centripeta tendente ad pun
Ctum citum extra rectam, secundum quam
Sold Vi insitd moreretur, (Ut PFOD. XXIX.
dictum:) ita Recta describetur à corpore
quod ursetur a Vi nulla tendente ad pun-
etum extra dictam Rectam situm: Nlam
Si manente utroque FIlipss rertice foci ad illos accedant, Fllipsis
in Rectam mutabitur. Ad reliquas omnes Lincas, praeter Rcctam e
Circularem, describendas, particulari opus eA L esC Vis centripeta.
LIOROI
(pex XVI. FI. 6.) CA eA ad eN ut XC ad 60; ergo e c ag ad Pxq
ut LC9 ad Ccg: LEt isitur ratie G ad eDg eadem est cum ra
Bet
Metr
Peto
Priu
cene
bo
tre
Catu
1