1. Giulio Carlo dei Toschi di Fagnano, Count and Marquis, was an Italian mathematician of the first half of the eighteenth century. He was one of the second generation of the followers of Leibniz, a generation rather pale and unimportant compared either with the first great founders of the Differential Calculus or with the third generation that dated from about the middle of the eighteenth century, of which Lagrange was the leading genius.

Several of the men of this second generation are known mainly for some one piece of work. This is particularly the case with Fagnano, who extended the application of the Integral Calculus to the rectification of curves in a way that may be regarded as the first germ from which afterwards sprang the Theory of Elliptic Functions.

Experiencing the well known difficulty of rectifying, by elementary integration, many curves whose equations seem, at first sight, easy to deal with, he showed that on some curves two arcs could be found whose difference was rectifiable ; although each separate arc presented the same difficulty as before.