I argued in Part II that Descartes' new account of matter, and his replacement of Scholastic material substantial forms with essential forms drawn from mechanics, stemmed from his project of providing mathematical demonstrations of physical phenomena. In the Discourse he justifies his new account indirectly by pointing to the explanatory success of scientific demonstrations based on suppositions about the essential forms of light, water, and salt. In The World he attempts to give a metaphysical grounding for his scientific demonstrations that does not yet indicate a commitment to the substance/mode ontology of his later metaphysical works. Rather, his project there resembles prior attempts to provide a more concrete (in this case, mechanical) analogue to the elemental forms of the Scholastics. As highlighted in the Introduction, Descartes was not the first to reject Aristotelian substantial forms. Moreover, my examination of his early scientific writings in light of his intellectual context reveals that he fully rejected them only late in his career, seeking first to unpack them in mechanical terms. I will now argue that the full metaphysical elimination of Aristotelian substantial forms characteristic of Descartes' mature philosophy had to await his response to standard skeptical arguments (of the kind marshaled by Sanchez) that preoccupied Mersenne. Descartes introduces two metaphysical doctrines to securely ground his scientific demonstrations and mathematical account of matter: the doctrine of the eternal truths of mathematics, and a substance/mode ontology like the one he would have encountered in his Dutch intellectual context. The second has the effect of eliminating material substantial forms.