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Euclid Book 5
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Euclid Book 5 Proposition 9b
Statement
I
f
a
m
a
g
n
i
t
u
d
e
h
a
s
t
h
e
s
a
m
e
r
a
t
i
o
t
o
t
w
o
o
t
h
e
r
m
a
g
n
i
t
u
d
e
s
(
E
F
A
B
E
F
C
D
)
,
t
h
o
s
e
m
a
g
n
i
t
u
d
e
s
a
r
e
e
q
u
a
l
(
A
B
C
D
)
.
Computational Explanation
G
e
o
m
e
t
r
i
c
S
c
e
n
e
{
A
.
,
B
.
,
C
.
,
D
.
,
E
.
,
F
.
}
,
{
x
.
,
y
.
,
z
.
}
,
S
t
y
l
e
[
L
i
n
e
[
{
{
A
.
,
B
.
}
,
{
C
.
,
D
.
}
}
]
,
R
e
d
]
,
S
t
y
l
e
[
L
i
n
e
[
{
E
.
,
F
.
}
]
,
B
l
u
e
]
,
E
u
c
l
i
d
e
a
n
D
i
s
t
a
n
c
e
[
A
.
,
B
.
]
x
.
,
E
u
c
l
i
d
e
a
n
D
i
s
t
a
n
c
e
[
C
.
,
D
.
]
y
.
,
E
u
c
l
i
d
e
a
n
D
i
s
t
a
n
c
e
[
E
.
,
F
.
]
z
.
,
z
.
x
.
z
.
y
.
,
E
u
c
l
i
d
e
a
n
D
i
s
t
a
n
c
e
[
A
.
,
B
.
]
E
u
c
l
i
d
e
a
n
D
i
s
t
a
n
c
e
[
C
.
,
D
.
]
,
x
.
y
.
C
o
n
c
l
u
s
i
o
n
E
u
c
l
i
d
e
a
n
D
i
s
t
a
n
c
e
[
A
.
,
B
.
]
E
u
c
l
i
d
e
a
n
D
i
s
t
a
n
c
e
[
C
.
,
D
.
]
Explanations
Let
C
have the same ratio to each of the magnitudes
A
,
B
; I say that
A
is equal to
B
.
For, otherwise,
C
would not have had the same ratio to each of the magnitudes
A
,
B
;
[
V
.
8
]
but it has; therefore
A
is equal to
B
.
Classes
Euclid's Elements
Theorems
Geometric Algebra
EuclidBook5
Related Theorems
EuclidBook5Proposition7
EuclidBook5Proposition9a
