In this case, I'd consider ancient to include 1300, because it was by comparison with the Enlightenment, as the time at which modern science began. I used the word to emphasise how relatively old it was.
I would agree it is most commonly used for examples like ancient Greece and ancient Rome which are older still.
Occam's razor is a very central concept in science and other rational discourse. It is remarkable that it is so ancient.
Not really, I'd consider "ancient" to be BC, but this was in the 1300s