Search results for "exactness problem"

Une quête d'exactitude : machines, algèbre et géométrie pour la construction traditionnelle des équations différentielles

2015

In La Géométrie, Descartes proposed a “balance” between geometric constructions and symbolic manipulation with the introduction of suitable ideal machines. In particular, Cartesian tools were polynomial algebra (analysis) and a class of diagrammatic constructions (synthesis). This setting provided a classification of curves, according to which only the algebraic ones were considered “purely geometrical.” This limit was overcome with a general method by Newton and Leibniz introducing the infinity in the analytical part, whereas the synthetic perspective gradually lost importance with respect to the analytical one—geometry became a mean of visualization, no longer of construction. Descartes’s…

Un delicato equilibrio tra macchine, algebra e geometria: Descartes e una possibile estensione differenziale