Archimedes was a real person, a mathematician and inventor, and didn't die in a battle, he was just killed, whereas Achilles was a legendary hero, and son of a goddess, who died in the Trojan war, which occurred (supposedly) a long time before the earliest Greek literature. Therefore, Achilles would have died hundreds of years before Archimedes was born. Klue, I wouldn't rely on Troy as a source of information about what happens in the Iliad.
While we're on the subject of heroes of the Trojan war, the phrase "between a rock and a hard place" is derived from an episode in the Odyssey when Odysseus must decide whether to sail his ship past the Syclla, a terrible creature that lives hidden, high on a cliff face (the "rock") or the Charybdis, an all-consuming whirlpool (the "hard place").
While we're on the subject of heroes of the Trojan war, the phrase "between a rock and a hard place" is derived from an episode in the Odyssey when Odysseus must decide whether to sail his ship past the Syclla, a terrible creature that lives hidden, high on a cliff face (the "rock") or the Charybdis, an all-consuming whirlpool (the "hard place").
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