In Chapter 21 of Vanden Circkel (On the Circle) [Van Ceulen, 1596], the arithmetic teacher and fencing master Ludolph van Ceulen published his analysis of 16 propositions which had been submitted to him by an anonymous “highly learned man”. In this paper, the author of the propositions will be identified as the classicist and humanist Joseph Justus Scaliger (1540-1609), who lived in the city of Leiden, just like Van Ceulen.

 The whole Chapter 21 of Van Ceulen’s Vanden Circkel turns out to be a criticism of Scaliger’s Cyclometrica (1594), a work which includes a false circle quadrature and many other incorrect theorems. The exchanges between Van Ceulen and Scaliger are analyzed in this paper and related to difference in social status and to different approaches to mathematics.