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# Title: Philosophical Principles Of Natural Religion (shelfmark Leibn. Marg. 53)
# Folio 47, page id 797370323:0487
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=797370323&page=487
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# 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.
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a iseile
a infinite
S OE, onc
Ole Sums
∞ 2=
d30
un infinité.
hatloever,
cheretore
beequal
ries; ptio
boch have
aulc, the
be infinite,
chC OnEA
Cor Fixem.
C.) CoCI.
+2 2
umberet
hetort Se.
rtes
ries encreales Palt, and alvrays doubles chie
precedins Term, and (0 quiekly arrives ac
∞ I. Whereas che sccond soes on ac che
Pame equable Race, (o chacchere is noc (0
ereac 2 Number oF Perms in che frst Series
25 in the second; For lec che Wumber oE
Terms ol a Geometricat Progression continu.
ed, bc, t che Ralio oF che Terms r, chc
preacest v, and cheleast an chen rV = ar.
and+=
t
in chis Case, Wrherer = 2,
a == 1, V = ∞. C, BecOIeS
L∞
22. NoW ie
is cerrain chacthe Loparirtm ot co, Isouly,
HDE infinitely lels, chanco; cheretore che
Number oF Terms, in che Arst Series, is Con-
Siderably lels, chan che Number oF T erIS
in che second Series. But Z. more parcieu.
Parly, in che drichmeticat Progrection ot na
Tural Numbers, beginins ac i and endins
aeo becaule chesum oF alI such is equat
eottie halF oF ehe Rectansle of the greacete,
into che sum of che Perms; cherelore +
F(2 +. 3 F 4 ]5 esc. concinued 10∞=
CoYCCMTL
because bochche last, and che Sum oE
1LSi13 (3 de 1631
the
2 12 1 3F
Loy. VL
L09.