Describe how Archimedes reacted to the reality of wartime in the Sand Reckoner?

Archimedes made practical inventions which enabled the Syracusans to fend off the Roman siege. He protected the city by his inventions, for example, he invented a huge crane operated hook " the claw of Archimedes" that could be able to lift enemy ships out of the sea. Legends tell that he also invented a way to make Roman ships to catch fire by reflection and focusing of light of the sun on their ships by use of a large mirror. A combination of this and onages and ballstats on the city walls made it difficult for Romans that forced them to apply direct assault which was expensive or the Romans.