| Figures which are similar to the same rectilinear figure are also similar to one another. | |
| Let each of the rectilinear figures A and B be similar to C.
I say that A is also similar to B. | |
| Since A is similar to C, it is equiangular with it and has the sides about the equal angles proportional. | VI.Def.1 |
| 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 and B is equiangular with C and with C has the sides about the equal angles proportional, therefore A is similar to B. | V.11 |
| Therefore, figures which are similar to the same rectilinear figure are also similar to one another. | |
| Q.E.D. | |
Book VI Introduction - Proposition VI.20 - Proposition VI.22.