# A differential extension of Descartes' foundational approach: A new balance between symbolic and analog computation

@article{Milici2020ADE, title={A differential extension of Descartes' foundational approach: A new balance between symbolic and analog computation}, author={Pietro Milici}, journal={Comput.}, year={2020}, volume={9}, pages={51-83} }

In La G\'eom\'etrie, Descartes proposed a balance between geometric constructions and symbolic manipulation with the introduction of suitable ideal machines. In modern terms, that is a balance between analog and symbolic computation. Descartes' geometric foundational approach (analysis without infinitary objects and synthesis with diagrammatic constructions) has been extended beyond the limits of algebraic polynomials in two different periods: by late 17th century tractional motion and by early…

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