Gottfried Wilhelm von Leibniz (1646–1716), philosopher and mathematician, born in Leipzig, died in Hannover, where most of his surviving manuscripts are kept. He was one of the founders of the important journal Acta Eruditorum (“Treatises of the Learned”) 1682. There he presented his theory of infinitesimals, differential calculus, in 1684.
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?