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Euclid Book 6
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Euclid Book 6 Proposition 12
Statement
G
i
v
e
n
t
h
r
e
e
l
i
n
e
s
e
g
m
e
n
t
s
,
t
o
f
i
n
d
a
f
o
u
r
t
h
s
u
c
h
t
h
a
t
t
h
e
l
e
n
g
t
h
o
f
t
h
e
f
i
r
s
t
i
s
t
o
t
h
e
s
e
c
o
n
d
a
s
t
h
e
l
e
n
g
t
h
o
f
t
h
e
t
h
i
r
d
i
s
t
o
t
h
e
f
o
u
r
t
h
.
Computational Explanation
G
e
o
m
e
t
r
i
c
S
c
e
n
e
M
.
,
N
.
,
P
.
,
Q
.
,
X
.
,
Y
.
,
A
.
,
B
.
,
C
.
,
D
.
,
E
.
,
{
}
,
L
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e
[
{
M
.
,
N
.
}
,
P
.
,
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.
,
{
X
.
,
Y
.
}
]
,
L
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e
[
{
{
A
.
,
B
.
,
C
.
}
,
{
A
.
,
D
.
}
}
]
,
E
u
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l
i
d
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a
n
D
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s
t
a
n
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[
A
.
,
B
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]
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u
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l
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D
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[
M
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,
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[
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,
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]
}
,
{
G
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t
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A
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n
[
{
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[
{
C
.
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.
}
]
,
L
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n
e
[
{
B
.
,
D
.
}
]
}
,
"
P
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r
a
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l
"
]
,
L
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e
[
{
A
.
,
D
.
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.
}
]
}
,
E
u
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l
i
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a
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D
i
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t
a
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[
M
.
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N
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]
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]
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[
X
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Y
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]
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D
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t
a
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[
D
.
,
E
.
]
S
t
e
p
1
2
3
4
C
o
n
c
l
u
s
i
o
n
E
u
c
l
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d
e
a
n
D
i
s
t
a
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c
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[
M
.
,
N
.
]
E
u
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l
i
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a
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D
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t
a
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[
P
.
,
Q
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]
E
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l
i
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a
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D
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t
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c
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[
X
.
,
Y
.
]
E
u
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l
i
d
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a
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D
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t
a
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[
D
.
,
E
.
]
Explanations
coming soon
Classes
Euclid's Elements
Constructions
Lines
EuclidBook6
Related Theorems
EuclidBook6Proposition11
EuclidBook6Proposition13
