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# Title: Philosophical Principles Of Natural Religion (shelfmark Leibn. Marg. 53)
# Folio 39, page id 797370323:0479
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=797370323&page=479
# Source image: https://digitale-sammlungen.gwlb.de/content/797370323/jpgs/default/00000479.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 47 lines, status machine
# Lines: 47 recognised, mean confidence 0.73
# 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.

et ci
find
in oF
F the
Ferene
Sutiro
141p3
tios
la 2 9
tromm
LL let
AI
5
0
luxal Bet
LF bC 1. AR = X,
atid the Lquation oF che Curve be y
an.
chen by che common Mechods ot Quadra.
cures, che indetinire Area ABCDFE L.K
6DeSE
Wrilt b0 X
-Bt
and che indetinire Area
2 XL n
AOLFEIRI erill be
E = B
Now il
n =ep chen the Lquation oF che Curve will
andche Area ABCDFLK Wrill
beequal co x.
- 1- + =
1 = 1 - f 1 -F B
+ 1.F, ec. concinved in infinicum, (ochae
Unier, is che infinitelr (maIL equal ParE, OF
che Area oF che Apollonian Fsyperbola. 
IF che Indetinice Area AC L FC RY BC
requird, chen (becaule X = y  In ChAE
B qu
Case) ic becomes
n and where p: = 1.
1- n
25 all0 n = 1 chat Area becomes
=_Y. 1 t 1 + 1 F 1, Xc. in infinitum, (0
chac iebisceridene, chacche space adiacen,
2
C CC4 241D9 2XH 310