Leibniz's differential calculus

Leibniz regarded curves as they were. The differentials dx or dy are infinitely small changes in the values of the variables x and y.

Equalities that were puzzling were x + dx = x and y + dy = y. The equals sign apparently assumes a new meaning together with differentials.

Guillaume de l’Hospital's Analyse des Infiniment Petits (published in 1696) was the first textbook on differential calculus. The book's first illustration shows Ap = x, PM = pR = y, Pp = MR = dx and mR = dy. It was highly criticized. Can we really see something that is infinitely tiny?