The refutation of Longomontanus' quadrature by John Pell

Summary

John Pell worked in the Netherlands from 1643 until 1652. He therefore deserves a place in a survey of mathematics c. 1650 in the Netherlands. During his stay he was mainly concerned with refuting a quadrature of the circle that was published in 1644 in Amsterdam by the Danish astronomer and mathematician Longomontanus. We therefore make Pell's refutation the main theme of this paper, but other aspects of Pell's work and some biographical information will be discussed within this framework. This paper includes a discussion of the refuted quadrature, and the first publication of a copy of the original one-leaf refutation, which was thought to be lost. In addition, we survey Pell's correspondence about the affair and in that connection discuss some unknown letters from Mersenne.