Michelangelo Ricci

Michelangelo Ricci investigated geometric problems of maxima and minima in the seventeenth century. A 1666 letter preserved by the Royal Society discusses his mathematical booklet and its argument concerning limits, providing contemporary evidence of its reception.^[ref]

A modern illustration of the relevant kind of optimization problem is to maximize $x^m(a-x{)}^n$ for $0<x<a$ and positive $m,n$. Differentiating its logarithm gives $m/x-n/(a-x)$, so the maximum occurs at $x=ma/(m+n)$. This calculation illustrates how a geometric extremum can become an algebraic relation; it does not attribute modern derivative notation to Ricci.