Earlier quoted context omitted.
They had nothing like the Modern age's science. I can't imagine any reason for it not appearing there given enough time, but they didn't have the dispassionate questioning of every theory and total submission to empiricism that are fundamental to science today. Math advanced a huge amount during the Medieval age. They simply didn't have good tools for calculations, and nearly all of the Modern Age's math was based on…
I find interesting that Archimedes came so, so close to calculus millenniums before Newton. I wonder how things would've panned out had him had the mathematical tools to formalize calculus.
As advanced as Ancient Greek mathematics was, its heavy emphasis on geometric formulations made many developments more difficult. The Hindu-Arabic numeral system, algebra, invention of a zero number concept (Cardan's proof of the cubic and quartic would have gone significantly easier if he had utilized zero as a number) and Descartes's Analytic geometry were important developments on the way to calculus. By the time of Barrow's and Fermat's contributions, nearly all essential components of calculus existed, just requiring some genius to grab, synthesize and streamline them.