An extremal problem in Harriot's mathematics (Q1121857)

The paper concerns two problems in Harriot's manuscripts which are variants of a problem arising from Harriot's construction to solve the spherical mirror problem of Alhazen's Optics. One involves maximizing a certain segment of a chord in a circle and the other the bisection of this segment by a radius of the circle. An elementary geometrical proof is given of the equivalence of the two problems. A second proof of the maximum intercept problem is then given using infinitesimal considerations similar to those used by Harriot in the problem of finding the change of longitude along a rhumb line.