You will see in that section a description of the range of activities to which fair use might apply, the logic of fair use in those situations, and most importantly, the limits on fair use. Look at how you are employing the illustrations, and whether your uses are within the limitations. For instance, is the connection between the image and your argument clear in the text?
If you are confident that your uses are within the terms of the Code, share your reasoning with peers and your publisher with confidence. Several publishers, including the College Art Association itself and Yale University Press, have already changed their permissions-only practice to one that encourages employing fair use.