 Leibniz’s calculus of differentials, resting as it did on somewhat insecure foundations, soon attracted criticism. The attack mounted by the Dutch physician Bernard  Nieuwentijdt[20]  (1654–1718) in works of 1694–6  is of particular interest, since Nieuwentijdt offered his own account of infinitesimals which conflicts with that of Leibniz and has striking features of its own (see Mancosu 1996: 158–160).  Nieuwentijdt postulates a domain of quantities, or numbers, subject to a ordering relation of greater or less. This domain includes the ordinary finite quantities, but it is also presumed to contain infinitesimal and infinite quantities—a quantity being infinitesimal, or infinite, when it is smaller, or, respectively, greater, than any arbitrarily given finite quantity. The whole domain is governed by a version of the Archimedean principle to the effect that zero is the only quantity incapable of being multiplied sufficiently many times to equal any given quantity. Infinitesimal quantities may be characterized as quotients \(b/m\) of a finite quantity \(b\) by an infinite quantity \(m\). In contrast with Leibniz’s differentials, Nieuwentijdt’s infinitesimals have the property that the product of any pair of them vanishes; in particular each infinitesimal is nilsquare, i.e., its square and all higher powers are zero (see Mancosu 1996: 159). This fact enables Nieuwentijdt to show that, for any curve given by an algebraic equation, the hypotenuse of the differential triangle generated by an infinitesimal abscissal increment \(e\) coincides with the segment of the curve between \(x\) and \(x + e\). That is, a curve truly is an infinilateral polygon.