Empiricism and common law versus rationalism and continental law.

Hello,
I would be happy to ask if the Rabbi knows of any writing (or of course whether the Rabbi has written himself) about the connection (if indeed it exists) between the developments in continental and common law, and empiricism and rationalism. Whether it is a historical connection, a conceptual one, etc.
I will try to explain briefly – to the best of my understanding (as much as I am wrong, I would be happy to understand), there is a central difference between the families of law that I mentioned above. While in the continental system, the method of legal thinking (in my understanding, at least in its essence) is characterized by abstract and systematic thinking (my addition – and perhaps one could even say “rational” that derives a solution to a concrete case from a general theory, deductive inference), while the common law system is characterized by an inductive method, which develops from case to case and derives the general accordingly (I consulted Aharon Barak’s article: “The Legal System in Israel – Its Tradition and Culture”). In my understanding, the aforementioned differences also characterize the dispute (of course in a rough and not concise generalization) between rationalism and empiricism regarding the manner of deducing information from reality, respectively. Furthermore, in my understanding, the place of development of these approaches is similar (mainly between common law and empiricism). While continental law developed primarily initially in the Roman Empire and then in Germany and France, similar to rationalism (at least in my understanding regarding Descartes and Leibniz), common law developed in Britain, similar to empiricism.
It is likely that I have made crude and inaccurate generalizations (including crude leaps in time and the reduction of thinkers of each system), but to the extent that I am fundamentally mistaken (likely with regard to the description of the connection between the Continent and rationalism – after all, the philosophical movement still existed in Greece), I would be happy to ask and point out whether the Rabbi knows of any writing that connects the development of empiricism with the development of common law, which is common to both approaches.
I hope I was able to clarify myself, and of course, thank you very much in advance and I wish you good news.