# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/797370323:0495
# Permalink to this reading: https://leibnizlegible.com/page/797370323:0495?run=74
# Title: Philosophical Principles Of Natural Religion (shelfmark Leibn. Marg. 53)
# Folio 55, page id 797370323:0495
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=797370323&page=495
# Source image: https://digitale-sammlungen.gwlb.de/content/797370323/jpgs/default/00000495.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 54 lines, status machine
# Lines: 54 recognised, mean confidence 0.80
# 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.

andeia
bexot
re Area
Bberbo.
onticts
RC. in
votrich
ot THC
SC, VetS,
an M.
in che
an che
e
ve af.
sCate,
Terms
an the
ippose
role 4.
in ehie
la
D
e
amibex
Dt saturat vet
Numbercot Verms in che ochers, wrhrole
Equal PaTIS are n 1 + n
u
1
n- +
ec. WHerE 2L  p be equal 10  e,
chen e muse be grearer chan a. Buc che
Pruch oF che Maccer i5, chac chelurencion,
Or che Cround oF che Discorerr, ot chele
equsl Pares; in chessimprocical Space oF chele
Fyperboloids, is chac cher all Aop, in cheir
yrequal Proprellions, dc ∞ 1. For Fxem.
DC, in che deries I f n + n L n3 ) n+
L n, esc. in infinitum, ertich expresses che
semptocicat Spaces AYF D C, the Invenriot
oF ies infinicely (maII ParE - depends up.
On the Supposicion, chac all chele Series sAop
ac ∞1, and 80 no turcher, Wrhereasro sive
cheerue FIyperbolick Spaces, cher must be aIl
supposd, 1090 on, an equal Number ot in-
finite Times. No lome ot em, divergine
lalter, chan ochers, (chole, viz. Wheren is che
oreacest Number) arrive ac co i Tooner, and
(0 by chele means an infinite Number oFchie
equal parrs, obcain d upon chis supposrion,
cannoc be cqual ro che infinitet umber ot un-
egual parrs wrhich constirure che area; thus
D d d 4
+