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# Title: Philosophical Principles Of Natural Religion (shelfmark Leibn. Marg. 53)
# Folio 48, page id 797370323:0488
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48
x
Dhuocorhilal
rinciples
the Terms is co; then as For che Geomerri-
cal Progrection ascendinq in infinitum, viz
1F 2 7 4 = 8 ec. usque ad ∞, IC is CVI
dene, every Term here is equal eo the sum
oF aIl cheFormer Y 1. and fince che la
Perm 15 supposd infinite, or ∞o 1, there-
Fore ∞o 1 = 1, I5 equal to the Sum oF all
the Forexoing Terms, and cheretore che lact,
Wich all che precedins, is equal 10 ∞ 1. 
∞ 1 =i =. (by che Rules oF Addition)
10 ∞ 2. in like manner in che Ceometrical
Progrettion concinually ascendine, trom 1
e0 c. ini chie Ratio OF E EO Z, ViZ. 1 +. Z
 9 + 27 esc. usque ad ∞. becaule every
Term = 1, is double oF all che precedine
Perms, and because chelast Perm is ∞ 1,
cheretore che Sum oF all che PermS excePE
∞
chelact, i5 = - 1; and consequenely che
Sum oF che last, and ot all che precedino
lerims, 15 ∞ 1. 
∞1
2
(by che
Rules ot Addition) ∞o Z. Wrhere ic is obser-
vable, chac che Series 1 + 2 F 4. ]. 8 e5c.
continued c0 x p. is grenter, chan 1 7 3
A
et
First.
eve
oFctic
chC
che Get
Ane
Ratio
5C
SuM
3C
che lal