 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, for instance, the curve \(y = x^2\). Given that the curve is an infinilateral polygon, the infinitesimal straight stretch of the curve between the abscissae 0 and \(\Dx\) must coincide with the tangent to the curve at the origin—in this case, the axis of abscissae—between these two points. But then the point \((\Dx , \Dx ^2)\) must lie on the axis of abscissae, which means that \(\Dx ^2 = 0\).