Some historians have speculated that classical Greek geometers used "hidden" analytic methods to discover results, which they then reconstructed synthetically. Further, it seems that Archimedes was further along towards calculus (though I gather this might be a bit exaggerated) than had been thought. In any case, the gradual decline of Aristotelean finitism and dismissal of empiricist epistemological constraints on geometrical reasoning in the 17th/18th century and the subsequent period of mathematical advance might be an instance of revitalization/rediscovery rather than of completely new developments, though these are claims in need of more careful historical argument than I'm in a position to give.