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.

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.*

Q.E.D.