Figures which are similar to the same rectilineal figure are also similar to one another.
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.
Q.E.D.