Controversy and modernity. John Wallis and the seventeenth-century debate on the nature of the angle of contact (Q2883430)

The nature of the angle of contact -- i. e., the angle between two curves touching each other or a curve and its tangent -- was a matter of considerable debate in mathematics before the rise of the differential calculus. The question was linked to the question on the nature of the infinitesimally small and thus had broader consequences for the validity of quadrature methods, for example. In an influential controversy in the 16th century, Peletier claimed that this angle was no quantity but just zero while his opponent Clavius held that the angle of contact could well be a quantity of a different kind than an ordinary rectilinear angle.NEWLINENEWLINEFrom his university lectures in 1652/3 to his correspondence with Leibniz at the turn of the century, John Wallis contributed with treatises and letters to the question. While his position seems clear and constant -- he sided with Peletier --, a remarkable turn took place in 1684 when he began to consider the angle of contact as a ``degree of curvity'', an interpretation, which he had ridiculed in 1666 after Hobbes had expressed it.NEWLINENEWLINEIn the present article the authors analyse the development of Wallis' view. By studying the context of his contributions they aim to give explanations for his continued interest in the matter and in particular his change of view. They convincingly argue that Wallis' reconsideration was prompted by the new infinitesimal methods. More specifically, they suggest an influence by Leibniz's differential calculus. But how and how much Wallis knew about Leibniz's calculus at the time remains unclear given that Leibniz published his first article on the subject only in October 1684.NEWLINENEWLINEFor the entire collection see [Zbl 1236.01002].