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Apart from works on geometry (such as Euclid's Elements and its various translations) and Spinoza's Ethics, has the axiomatic method been used as a means of exploring a certain field or exposing one's thesis? Any examples would be very useful.

I have searched for "ordine geometrico" (which is Latin for "geometric method") on various places online such as Archive.org and Gallica, but all I can find are references to Spinoza.

The relevant Wikipedia entry mentions nothing between Euclid and the 19th century.

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Cavalieri's book Geometria indivisibilibus continuorum nova quadam ratione promota (1637) was written in such an axiomatic style. Cavalieri was particularly concerned to present his work in a rigorous style because at the time indivisibles and atomism were under ferocious attack by the catholic hierarchy in general and jesuits in particular. A useful study of Cavalieri by Hector Manuel Delgado (2017) is now accessible on the web.

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I recall a peculiar physics book

Information Mechanics by Frederick William Kantor (1977)

He starts with some simple axioms on information and (in 100s of pages of deductions) ends up doing physics ??

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Of course, Hilbert, Grundlagen der Geometrie, published in 1899 (Engl. Tr. The Foundations of Geometry).

The Grundlagen contain an axiomatic exposition of geometry in purely synthetic terms. The purpose of the book, as Hilbert says in the introduction, is “to establish for geometry a complete system of axioms”:

Geometry requires, […] to be coherently founded, only few, simple fundamental propositions. These fundamental propositions are called the axioms of geometry.[…] This investigation is a new attempt to establish for geometry a complete system of axioms and as simple as possible, and deduce from them the most important geometric propositions, in order to highlight clearly the meaning of the different groups of axioms and the scope of the consequences to be drawn from the single axioms. .” (Hilbert, cit. Introduction, my tr.)

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  • $\begingroup$ Frege, too, for a similarly-axiomatic attack on arithmetic/number theory? $\endgroup$
    – nitsua60
    Commented 2 days ago
  • $\begingroup$ Yes, axiomatic method was invoked also for arithmetics and number theory, also by Hilbert, think for instance of the axiomatic definition of real numbers. $\endgroup$
    – BakerStreet
    Commented 2 days ago

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