Under Development
A collection of classical geometry in computable formats along with code and diagrams.
Computable Euclid
›
Euclid Book 5
›
Browse books
Euclid Book 1
Euclid Book 2
Euclid Book 3
Euclid Book 4
Euclid Book 5
Euclid Book 6
Euclid Book 13
Euclid Book 5 Proposition 4
Statement
Computational Explanation
Explanations
For let a first magnitude
A
have to a second
B
the same ratio as a third
C
to a fourth
D
; and let equimultiples
E
,
F
be taken of
A
,
C
, and
G
,
H
other, chance, equimultiples of
B
,
D
; I say that, as
E
is to
G
, so is
F
to
H
.
For let equimultiples
K
,
L
be taken of
E
,
F
, and other, chance, equimultiples
M
,
N
of
G
,
H
.
Since
E
is the same multiple of
A
that
F
is of
C
, and equimultiples
K
,
L
of
E
,
F
have been taken, therefore
K
is the same multiple of
A
that
L
is of
C
.
[
V
.
3
]
For the same reason
M
is the same multiple of
B
that
N
is of
D
. And, since, as
A
is to
B
, so is
C
to
D
, and of
A
,
C
equimultiples
K
,
L
have been taken, and of
B
,
D
other, chance, equimultiples
M
,
N
, therefore, if
K
is in excess of
M
,
L
also is in excess of
N
, if it is equal, equal, and if less, less.
[
V
.
D
e
f
.
5
]
And
K
,
L
are equimultiples of
E
,
F
, and
M
,
N
other, chance, equimultiples of
G
,
H
; therefore, as
E
is to
G
, so is
F
to
H
.
[
V
.
D
e
f
.
5
]
Classes
Euclid's Elements
Theorems
Geometric Algebra
EuclidBook5
