"...A type of crossbow used by the Chinese since at least 210 B.C. was a repeating design with a gravity-fed box magazine!..."

There was a chap in Britain who built an automatic/semi-automatic heavy cross-bow (ballista?) based on Roman writings of 1st Century AD(no drawings, so a little speculative).
As I recall, this also has a box magazing but with a rotary cylinder feed for the bolt.
The weapon worked by cranking a handle forward to pick up the string then back to tension the string and loose the bolt ('fire the weapon' didn't seem quite right). When they demonstrated the weapon on TV (albeit with much reduced tension on the arms) they were getting a rate of about 12 rounds per min and very close grouping.

Regards

Walrus