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.
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.
Therefore, figures which are similar to the same rectilinear figure are also similar to one another.