Linné on line Mathematics in Linnaeus’ time The infinitely small 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?