If a cubic number does not measure a cubic number, then neither does the side measure the side; and, if the side does not measure the side, then neither does the cube measure the cube.

Let the cubic number *A* not measure the cubic number *B,* and let *C* be the side of *A,* and *D* of *B.*

I say that *C* does not measure *D.*

For if *C* measures *D,* then *A* also measures *B.* But *A* does not measure *B,* therefore neither does *C* measure *D.*

Next, let *C* not measure *D.*

I say that neither does *A* measure *B.*

If *A* measures *B,* then *C* also measures *D.* But *C* does not measure *D,* therefore neither does *A* measure *B.*

Therefore, *if a cubic number does not measure a cubic number, then neither does the side measure the side; and, if the side does not measure the side, then neither does the cube measure the cube.*

Q.E.D.

“Contrariwise,” continued Tweedledee, “if it was so, it would be; but as it isn’t, it ain’t. That’s logic.”