Manuscripts on the Foundations of Geometry
In this section we present a collection of texts written by Leibniz on several topics in elementary geometry. Leibniz worked at the foundations of geometry throughout his life, and left many hundreds of pages and manuscripts on this subject. Almost none of them were published in his lifetime, and only a few are currently available in print. Leibniz’ studies on the foundations of geometry deal with a vast array of topics: history of mathematics, commentaries on Euclid’s Elements, philosophical discussions on definitions of basic geometric figures, new developments of axiomatics, formalization of geometry through different symbolic systems (a characteristica geometrica), new proofs of well-known theorems, discussions on diagrams and their role in mathematics, foundations of higher mathematics in elementary geometry, and much more. Sometimes, Leibniz labeled the whole of these researches with the general name of analysis situs, and this new discipline stays at the crossroads of mathematics, logic, epistemology and metaphysics of space. Leibniz’ analysis situs is likely to be the highest point of foundational research in mathematics in the 17th century.