This chapter is about atomism. Apparently atomic ideas held a place of prominence in Islamic science, for theological reasons, but were marginal in Greek science because Aristotle rejected them. It is thus hard to argue that atomism in modern science is a Greek legacy. More interestingly, the Arab philosopher Averroes argued in favor of Aristotle and in the process offered an argument in favor of science and against clerical philosophy, one taken up by European scholars to the alarm of the Church. Ironically, his defense of incorrect science was used to carve out a space in which science could eventually thrive.
However, given the paucity of evidence for atoms during the time in question (my recollection is that evidence for them didn't really come into play until the 18th century) it is hard for me to treat older ideas for or against atoms as no more than wildass speculation. Like string theory.