![]() ![]() In the late 17th century, the synthetic aspect was extended by “tractional motion” (construction of transcendental curves with idealized machines). Descartes’s foundational approach (analysis without infinitary objects and synthesis with diagrammatic constructions) has, however, been extended beyond algebraic limits, albeit in two different periods. 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. In particular, Cartesian tools were polynomial algebra (analysis) and a class of diagrammatic constructions (synthesis). ![]() In La Géométrie, Descartes proposed a “balance” between geometric constructions and symbolic manipulation with the introduction of suitable ideal machines. ![]()
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