×

John Wallis: Lectures on the polemics between Peletier and Clavius on the angle of contact. (Italian) Zbl 0935.01003

Galuzzi, Massimo (ed.), Conference on the history of mathematics. Papers from the conference, Cetraro, Italy, September 8-12, 1988. Rende: Editoria Elettronica, Semin. Conf. 7, 315-364 (1991).
In his introduction the author calls attention to the fact that repeatedly certain historical events are submitted to different interpretations in the course of time. As an example, he analyzes the dispute between Jacques Peletier (1517-1582) and Christoph Clavius (1537-1612) on the angle of contact, that took place in the second half of the 16th century, and the interpretation John Wallis (1616-1703) gave about a century later. Wallis published his De Angulo Contactus et Semicirculi, Disquisitio Geometrica in 1656, and he returned to the problem in A Defense of the Treatise of the Angle of Contact in 1684 (issued as appendix to his A Treatise of Algebra, London 1685). The angles under consideration are (i) the angle of contact between a circle and its tangent line at the point of contact, and (ii) the angle between the diameter of the circle ending at the point of contact, and the circular arc. The question whether these angles are comparable to angles between two straight lines or, if not, what their nature is, had already occupied medieval mathematicians. Peletier (Peletarius) maintained that the angle of contact is heterogeneous to a rectilinear one (as is a line to a surface), while Clavius denied this. Wallis took sides with Peletier and, in his Defense, attacked not only Clavius but also his fellow Jesuit Vincent Leotaud (1595-1672) as well. The present article analyzes in detail first the contents of the Disquisitio Geometrica, then the Defense. In his conclusion the author emphasizes the substantial shifts of Wallis’s attitude: in his first tract he paid much attention to Euclid’s struggle with the problem and to arguments put forward by Clavius, in the second he tried to express the ancient problem in new terms, such as inceptive, evanescent, or infinitesimal quantity. Of special interest to the modern reader may be the emphasis he put on the non-Archimedean property of angles of contact. — Fourteen pages of detailed notes enhance the value of this thorough investigation.
For the entire collection see [Zbl 0903.00033].

MSC:

01A40 History of mathematics in the 15th and 16th centuries, Renaissance

Biographic References:

Wallis, J.; Peletier, J.; Clavius, Chr.
PDFBibTeX XMLCite