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Film of a bunch of animals and crew members sun bathing and snoozing on the 80-year-old fishing boat during the experiment at 11.
Lets give old Archimedes his due: the man was smart, obviously smarter than the Mythbusters, because he wouldn't have tried to set the wood on the ships afire because that would be too hard--even if the tests proved it could be done.
Nope, Archimedes would have targeted the most vulnerable part of the ship--the sails. Cloth is much more susceptible to combustion due to high heat that denser wood.
But if you get flaming sails falling upon decks which are caulked with tar and containing jars of oil for cooking and possibly for use in naval warfare, then you have a serious chance of making your weapon work.
And even if it only destroys a ship or two, the written record becomes pumped up by overwrought reporters and survivors.
Compare the records of two ancient inventions. No one ever claimed that Da Vinci ever made his aeroplane actually fly--and the blueprint plans don't work when they are completed. But even in this test, fires were started, proving that the history of Archimedes feat is possible.