# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/797370323:0481
# Permalink to this reading: https://leibnizlegible.com/page/797370323:0481?run=74
# Title: Philosophical Principles Of Natural Religion (shelfmark Leibn. Marg. 53)
# Folio 41, page id 797370323:0481
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=797370323&page=481
# Source image: https://digitale-sammlungen.gwlb.de/content/797370323/jpgs/default/00000481.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 59 lines, status machine
# Lines: 59 recognised, mean confidence 0.70
# 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.

Moniar
SpACC
cOmes
DEL
+ f 8
de
BOIsD
l10.
51P
ic DC
finite-
1
Arti. 
ex otocn
Ouldpo 21
bolick
FF
1091
= 1a I3IM
+1
D
Satural Peligion.
+
8 Cac. Whole hrsc Term is
and last 0, and the Ratio ot the Perms knc
10 7, Ox 2 10 1, cheretore by che precedine
arcicle, che sum oF che Terms is
L = 20
50 chac che whole ssimptoricat Space oF
che Fyperbola Wrhole L. quation I5 y X = 1.
Wrould bc ∞ 2 4. 2 = ∞ 2, upon sup.
polirion chac che grearest Term oE its un
equal Prooression ivere only Intinice or c
IFn = 3 and X = 1. then the Area ATF D 61O
13 =  + 3 + 9 F27,85c. = (by chein 5
precedinq Section) 2 + 2 + 2
2
esc.
Wrhen che last Ferm is ouly ∞o 1. aHd iF
s
n = 3, and 1 = 1, che Area AB P F LP 3BNI
3-eF  Y  in f = 
ea
2y ec. and che
irtiole ssymptorick Space oF chis FSyperboloid,
15 Cqual EO ∞ 2  2 1 2
2
f. 2 + 3
2
23185C.
s
3c
upon chac suppolicion. Anduniverlaily, eg
AV
iCX = 1, chen che SpaCC AIFDC =
1 + n -) n Y n + nt, esc. Whole intru.
nicely. Imalb equal pare (suppolins che laH
Perm oE cheSeries omly ∞ 1.) by che pre-
cedinq