By then, Arabs had the catapult. We probably got it from them during the Crusades, but we only used it for a little while. We soon gave it up for another Chinese invention. In the 1300s, we took up firearms. For the simplicity's sake, I've used the familiar word catapult .
Historians prefer to use the French word trebuchet .
The correct term for the counterbalanced lifting device is swape . The swape lets you divide the force of lifting in two. Typically, to lift 80 pounds of water, you would push the bucket down into the water with a 40 pound force. Then it would take a 40 pound force in the other direction to lift the filled bucket. I am grateful to Pat Bozeman, Head, Special Collections, UH Library, for drawing my attention to this uncatalogued source and making it available to me.