![]() 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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