The author set himself an ambitious goal of webbing an intricate story about Western physics from Aristotle to Lagrange. Good story-telling starts with something familiar, seemingly truthful to the reader, that is yet (partially) wrong or incomplete (unknown to the reader). And through the story, the reader gains wisdom by being surprised of something new that (partially) falsifies their current body of knowledge.
The author starts with something that the modern-day reader knows to be wrong, and ends with a dubious conclusion (that somehow the variational principle validates Aristotelian teleology).
A good story would start with the Newtonian mechanics, the prevailing view among those who did not study physics at the university. The author does not need to heed my amateur advice: He can attack strawmen, i.e. valid yet superfluous, off-target criticisms.