Sir, wut? Bows were never forbidden afaik, only crossbows were first considered non-christian weapons due to how easy it was for a common peasant to kill a nobleman with no training at all.
Or prove me wrong, and give me some stuff to read so I can re-educate myself.
Got these infos from wiki. It was at the Second Council of the Lateran 1139 where the ban happend. But I just stumbled over a big difference between the german and the english wiki version.
The german version states that canon 29 forbides bows and xbows to be used against christians.
the english version says "The council also may have banned the use of crossbows against Christians,[2][3] although the authenticity, interpretation and translation of this source is contested."
So somebody has to do some further research.
