Similarly, the symmetry of the infinitesimal strain tensor implies that . It is an extension of the reals obtained by including infinite and infinitesimal numbers. The goal is to divide the original volume into infinitely many infinitesimal volumes. The curvature arises when one travels around an infinitesimal parallelogram. The first theorem exhibited the basis of an algebra through infinitesimal transformations. The original formulation of infinitesimal calculus by Isaac Newton and Gottfried Leibniz used infinitesimal quantities. Synthetic differential geometry or smooth infinitesimal analysis have roots in category theory. Descartes' book became famous after 1649 and paved the way to infinitesimal calculus. This played a key role in the emergence of infinitesimal calculus in the 17th century. However, this figure relies on the assumption that space can be subdivided into infinitesimal sections. This in turn makes it possible to represent infinitesimal spatial rotations and Lorentz boosts. He also studied Isaac Barrow and John Wallis, leading to his interest in infinitesimal geometry. This in turn led to innovative developments in infinitesimal geometry. An ideal dipole consists of two opposite charges with infinitesimal separation. It turns out that "the order in which infinitesimal rotations are applied is irrelevant".