What weapons would a mathematician in the 1600s invent?

We see that very question answered in the Second Punic War, the Roman’s attack Carthage’s fort on the island of Sicily, also the home of Archimedes.

The siege was a multi month affair.

At his creativity the claw of Archimedes, and, hypothetically, a giant mirror directed at the sailed of ships were used.

And so impressive were these tools of defense that the Roman proconsul Marcellus instructed his army to spare his life