Outdoing John Henry's "The Scientific Revolution and the Origins of Modern Science" would not be easy. The function of the work is to bring the reader up to speed on the "state of the debate," as he says in the preface. Moreover, it has the overtly pragmatic function as a bibliographical guide for anyone, the student or general reader, to the key resources necessary to fast-track research and get one's feet wet with the "key" works. Beyond that, the text is a pleasant read, focusing on amorphous nature of pre-science that crystalizes into early modern science. Important elements highlighted in this amorphous miasmic pre-science cloud of practices are descriptively religious, mathematical, material procedural (method and experiment), philosophical (esp. mechanical), and magical in nature. As with any survey, the text presents a study that is by no means systematic. In my judgment, John Henry does draw out those features of the period that spring to mind as being the most salient. Even though not systematic, I think Henry does well to tie themes together and develop a large-scale picture of what's going on (primarily) in the sixteenth and start of the seventeenth century. As far as existing scholarship goes, the author does make clear that much, much more research on the relation between mathematics, magic, and science is needed, a truism I have found in history of mathematics literature.
The book definitely has some shortcomings. For example, in chapter 3 (pg. 43 of 1st edition), he says, "The pragmatism of magic is obvious." That's definitely not the case for the student. From my perspective, a contemporary philosopher of science with some training in history, having only been recently introduced to primary sources in magic, see little of pragmatic value in many of the magic texts. Many magicians did not even espouse to have performed any of the "recipes" that they had written down. Other texts espouse functional utility, but, in some cases, it is still unclear whether the rituals, etc., were ever performed by a single soul. It is clear that procedures from other texts were performed, and efficaciously so. For this reason, I wished Henry had not made the half dozen, or so, unsupported statements that occur throughout the text. There are a few other little details, but they make no significant detraction from this very valuable and well-written text.