John Wallis and the “Rectification” of the Parabola

Abstract

The problem of the rectification of curves and the calculation (for which we shall adopt the more geometric term “flattening”) of the surface of a rotating solid generated by a curve, once the rotation axis has been fixed, were treated by John Wallis in two short inter-related tracts on cycloids and cissoids in 1659. In this work, we focus on the problem of the rectification of the parabola, an ancient problem reproposed in the 17th century, and on the solution obtained by Wallis using particular series that reflect the mechanical method of Archimedes, even if this is not immediately apparent to the reader. In presenting Wallis’s speech, we use the language closest to us and make explicit all the calculations not performed by the author, favoring an understanding of the part of his writing dedicated to the rectification of the parabola.