 René Descartes (1596–1650) employed infinitesimalist techniques, including Cavalieri’s method of indivisibles, in his mathematical work. But he avoided the use of infinitesimals in the determination of tangents to curves, instead developing purely algebraic methods for the purpose. Some of his sharpest criticism was directed at those mathematicians, such as Fermat, who used infinitesimals in the construction of tangents.