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A collection of classical geometry in computable formats along with code and diagrams.

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Euclid Book 6 Proposition 21

Euclid Book 6 Proposition 21

Statement

Polygons which are similar to the same polygon, are similar to one another.

Computational Explanation

GeometricSceneA.,B.,C.,D.,E.,F.,G.,H.,I.,{},GeometricAssertionTriangleA.,B.,C.,TriangleG.,H.,I.,"Similar",GeometricAssertionTriangle[D.,E.,F.],TriangleG.,H.,I.,"Similar",GeometricAssertionTriangleA.,B.,C.,Triangle[D.,E.,F.],"Similar"

GeometricAssertionTriangleA.,B.,C.,TriangleD.,E.,F.,Similar

Explanations

For let each of the rectilineal figures

A

,

B

be similar to

C

; I say that

A

is also similar to

B

.

For, since

A

is similar to

C

, it is equiangular with it and has the sides about the equal angles proportional.

Again, since

B

is similar to

C

, it is equiangular with it and has the sides about the equal angles proportional.

Therefore each of the figures

A

,

B

is equiangular with

C

and with

C

has the sides about the equal angles proportional; therefore

A

is similar to

B

.

Classes

Euclid's Elements
Theorems
Polygons
EuclidBook6

Related Theorems

EuclidBook6Proposition4
EuclidBook6Proposition5
EuclidBook6Proposition6
EuclidBook6Proposition7a
EuclidBook6Proposition7b