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A collection of classical geometry in computable formats along with code and diagrams.
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Euclid Book 6
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Euclid Book 6 Proposition 17b
Statement
Computational Explanation
Explanations
Let the rectangle
A
,
C
be equal to the square on
B
; I say that, as
A
is to
B
, so is
B
to
C
.
For, with the same construction, since the rectangle
A
,
C
is equal to the square on
B
, while the square on
B
is the rectangle
B
,
D
, for
B
is equal to
D
, therefore the rectangle
A
,
C
is equal to the rectangle
B
,
D
.
But, if the rectangle contained by the extremes be equal to that contained by the means, the four straight lines are proportional.
[
V
I
.
1
6
]
Therefore, as
A
is to
B
, so is
D
to
C
.
But
B
is equal to
D
; therefore, as
A
is to
B
, so is
B
to
C
.
Classes
Euclid's Elements
Theorems
Geometric Algebra
EuclidBook6
Related Theorems
EuclidBook6Proposition16a
EuclidBook6Proposition16b
EuclidBook6Proposition17a
