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. (shrink)

A letter written by Christiaan Huygens to David Gregory is published here for the first time. After an introduction about the contacts between the two correspondents, an annotated English translation of the letter is given. The letter forms part of the wider correspondence about the ‘new calculus’, in which L'Hospital and Leibniz also participated, and gives some new evidence about Huygens's ambivalent attitude towards the new developments. Therefore, two mathematical passages in the letter are discussed separately. An appendix contains the (...) original Latin text. (shrink)