Archimedes used cannons, not mirrors to burn Roman ships

Other advanced Greek technology was lost and unmatched again for centuries. Note the Corinthian connection in the origins of the Antikythera mechanism. http://en.wikipedia.org/wiki/Antikythera_mechanism#Origins

However, whilst lost to the West, many of these traditions lived on in the Byzantine Empire and Arabic automatons and inventions (Al-Jazari), so there is some continuity. The migration of Greek scholars and texts from Byzantium to Italy at the behest of philhellenic sponsors then sets the stage for Da Vinci and others as the article notes. If anything it serves as a reminder that high technology and culture can be lost in the vicissitudes of human arrogance, conflict and oppression.

Although confined to the elites the Greeks knew the earth was round, and they had a theory of evolution and complex mechanical computation devices. Today we battle against people trying to insert creationism into schools and a massive and systemic attempt across the West to censor and control the Internet. The only thing we can be thankful for is that the flat-earth movement can't get any traction in the face of satellite imagery (although, the moon landing hoaxers are not too far off such a proposition and get quite a few people to believe them).