Another point that Grant makes is that it’s very difficult to actually say what Aristotelian philosophy was as it changes constantly throughout the High Middle Ages. That Aristotelian Philosophy was some sort of unchanging, unchangeable monster cast in concrete by the Catholic Church with an injunction against all forms of inquiry is a myth perpetuated by people who believe in the Draper-White hypothesis of an eternal war between science and religion.The last paragraph hits on an interesting point: science texts are generally just terrible on history. I think the problem is to some extent ideological, in that many of the writers want to believe the positivist story of science, but also is due to the fact that many people are not aware that historical facts are discovered by historians. So it is now "beyond contention" that advances still being attributed to Galileo were actually made in the 1300s: a newly discovered fact. I imagine that many writers of science textbooks think that historians start with facts and then weave "historical theories" around them, and so it wouldn't even occur to them that what was thought to be fact when they were in college has since been proven false.
Let us look at a specific example of that process of change; in fact an area that would play a central role in the creation of modern science in the Early modern period, the laws of motion. Already in the sixth century CE John Philoponus criticised Aristotle theory of motion and introduced the concept of impetus. This stated that the thrower imparted a motive force to the thrown object, impetus, which decreases over time till the object stops moving. Via the Islamic thinker Nur ad-Din al-Bitruji in the twelfth century the theory was taken up and elaborated by Jean Buridan in the fourteenth century and through him entered mainstream Medieval thought. The theory of impetus played a central role in the early considerations of both Giambattista Benedetti and Galileo who developed the modern laws of fall. The seventeenth-century theory of inertia, Newton’s first law of motion is in reality a consequent development of the theory of impetus.
Also in the fourteenth century the so-called Oxford Calculatores developed mathematical quantified version of Aristotle’s theories, in particular deriving the mean speed theorem, which lies at the heart of the laws of fall. The Paris physicists took up this work and produced graphical representations of the mean speed theorem identical to the ones presented later by Galileo. To quote historian of mathematics, Clifford Truesdall:
The now published sources prove to us, beyond contention, that the main kinematical properties of uniform accelerated motion, still attributed to Galileo by the physics texts, were discovered and proved by scholars of Merton college…. In principle, the qualities of Greek physics were replaced, at least for motions, by the numerical quantities that have ruled Western science ever since. The work was quickly diffused into France, Italy, and other parts of Europe. Almost immediately, Giovanni di Casale and Nicole Oresme found how to represent the results by geometrical graphs, introducing the connection between geometry and the physical world that became a second characteristic habit of Western thought...