If the curve y = x² is an infinilateral polygon, then the infinitesimal straight stretch of the curve between abscissae 0 and Dx coincides with the tangent to the curve at the origin.

In responding to Nieuwentijdt’s assertion that squares and higher powers of infinitesimals vanish, Leibniz objected that it is rather strange to posit that a segment \(\Dx\) is different from zero and at the same time that the area of a square with side \(\Dx\) is equal to zero (Mancosu 1996: 161). Yet this oddity may be regarded as a consequence—apparently unremarked by Leibniz himself—of one of his own key principles, namely that curves may be considered as infinilateral polygons. Consider, fo