Descartes’ first studies of Pappus’ problem (early 1632)

Abstract

Sometime in late 1631 the Dutch mathematician and philologist Jacob Van Gool (Golius) suggested to Descartes that he should try his new method in solving the problem, mentioned by Pappus, of the locus to three, four, or more lines. This is the problem that, through Descartes’ treatment of it in the Geometry, has become famous as “Pappus’ problem.” The texts of two letters¹ of Descartes to Golius about the problem have survived. From the one, written January 1632, it appears that he had sent Golius an “écrit” (manuscript) containing his solution of the problem, and that he hoped to receive comments. The écrit itself is lost, but Descartes’ first letter contained an addition to it. In the second letter, dated February 2, 1632, Descartes merely expressed his gratitude for Golius’ “favorable judgment” upon his solution of the problem.