If one is going to use modern technology to do Archimedes's Death Ray "right", one might has well go all the way and use a laser, perhaps having it be solar powered as a nod to the original design.
Use automatic visual tracking to keep the narrow laser beam on the exact same spot on the ship's hull as it moves, heating the wood to the point of ignition. This probably requires a much less powerful laser than a weapon to directly vaporize a human.
It does not need to be dawn to defend Syracuse.
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