# Servois' 1814 Essay on the Principles of the Differential Calculus, with an English Translation - Limits and Infinitesimals

Author(s):
Wronski was a Kantian and Servois began his philosophical refutation of Wronski's position by exhibiting his own knowledge of Immanuel Kant's philosophy, attempting to use it to buttress his position on the inappropriateness of the use of infinite in mathematics. He further challenged his readers to examine the principle that if $$dz$$ is an infinitely small quantity of the first order, then $$d^{2}z$$ is one of the second order. Servois claimed that it is easy to demonstrate this by using Taylor series, but impossible with the infinitely small. Servois continued his critique, eventually concluding that infinitesimals “will one day be accused of having slowed the progress of the mathematical sciences, and with good reason” [Servois 1814b, p. 148].