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# Title: Philosophical Principles Of Natural Religion (shelfmark Leibn. Marg. 53)
# Folio 64, page id 797370323:0504
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54 DGnotorhical Brinciples
Poines at che Pertex common wich che orhee
Curve, and consequendy 2r X  a = i
N  X
andr =X
de
Ln - 2 - X
S0 chen
itm = 1, che Curve becomes che Appollonian
Parabola, andr =
- 2
X
+ x.
buc in ehis case r is infiniclr small in respect
ot any finite quancier, and loisto bechromn
avay andr becomes = 1. e. The Radius oF
 Circle, that has che lame deorec ot Curva.
cure, Wich ehe appollonian Parabola, is equal
co one halF oFies Latus rectum. II m L F,
4m - 
ehcar =
~ = 0, For in chat C asC
un-. is infinitly (mall in respeet ot i, and x
is eo be suppos do, or infinitty (mall, ertien
x is a Aorine Ouanciey. Wheretore che
Radius AD is infinitls (mall, or cheCurva-
ture ot such Curves ABO, is infinitly greae
ac chePertex, in respeet ol che Curvature ot
the Circle, or berreen che Tangent AF, and
bbru ehe Curve AB s Circle can FaI1, IF m  13
chenr
1+ v
= ∞. For in chaE
Cale
t
che le
CmalI.
Coche
tex, 15
thC Cu
dOr
couche
OFche
AB V
Circle
1
F.X
C
n C
en
eset
urhose