Leibniz recognized the need for differentials but not nilsquare infinitesimals, while Nieuwentijdt recognized nilsquare infinitesimals but not differentials.

Now Leibniz could retort that that this argument depends crucially on the assumption that the portion of the curve between abscissae 0 and \(\Dx\) is indeed straight. If this be denied, then of course it does not follow that \(\Dx ^2 = 0\). But if one grants, as Leibniz does, that that there is an infinitesimal straight stretch of the curve (a side, that is, of an infinilateral polygon coinciding with the curve) between abscissae 0 and \(e\), say, which does not reduce to a single point then \(e