Archimedes died defending the ancient city of Syracuse, on the island of Sicily, from the Carthaginian navy. Reports attributed the defense of the city to his ingenuity, including giant mirrors capable of setting attacking ships in the harbor on fire. Renaissance scientist-engineers applied the Conic Sections of Apollonius to help them understand whether and how burning mirrors and other optical effects might be achieved using parabolic, hyperbolic or elliptical surfaces. Galileo’s interest in lens grinding helps explain why he regarded Cavalieri as one of the greatest geometers since Archimedes. Cavalieri, a theologian and mathematician, studied at Pisa with Castelli, one of Galileo’s students, and engaged in extensive correspondence with Galileo.