Roberval worked on his Elements of geometry for several years. The treatise was almost finished when, in 1675, the author died. In my paper, I intend to discuss the first book of Roberval's treatise insisting on the foundational ideas on which it is based. He deals with the "principles and axioms", and wants to give demonstrations for many propositions generally accepted without demonstrations. The fundamental themes are the logical relations of equality and inequality and the relations between a whole and its parts. They are treated in 6 definitions, 4 axioms, 2 postulates and finally in the 30 theorems of this first book.
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