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Linné on line arrow Mathematics in Linnaeus’ time arrow The infinitely small arrow Leibniz's differential calculus

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?

Analyse des Infiniment PetitsGraphs describing Pp = MR = dx and mR = dy