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First of all the Athenians did not win the battle of salamis, the Greeks did and they won because they had smaller and faster Greek ships
They had smaller boats and were eaiser to control.
their large area of land
Because Salamis was a sea battle, and the Greek side woulld be at a bit of a disadvantage without ships.
Control of the sea and blockade of the Persian sea resupply from Asia Minor.
stagey*
By duping the Persians into splitting their forces so that a third of their navy was not present, and catching them badly dispersed in two narrow straits and engaging and overcoming them piecemeal.
Superior strategy they split the Persian fleet so that a third of it was not present at the battle, so evening up the numbers of ships on either side. Superior tactics - they engaged the Persian fleet when it was strung out coming around an island in the middle of the strait st Salamis.
It didn't with the first encounter in the naval battle they knew they had to win at Artemesium resulted in their defeat. They tried again at Salamis in a better area which split the Persian fleet and won.
At the Battle of Salamis, the Greek ships were built specifically for fighting at sea, whereas the Persian ships were not, and also the Greeks were much better sailors. The mast and sails were taken down and stowed for fighting, and the ships were maneuvered entirely by the oarsmen. The Persian ships were sunk by ramming them.
They did not, the Persians won; the Greeks were WAAY outnumbered.
They were part of an alliance of 20 city-states led by Sparta which induced the Persian fleet to split up and enter a narrow strait in line-ahead, where the Greeks pounced on them from the flanks and destroyed them.