Introduction

In this paper our interest is not in a renowned mathematician, a celebrated school, or a famous problem, but in a curve, the cycloid. More particularly, our interest is to center around its relation to the mathematics of the seventeenth century, one of the great centuries in the history of the subject. This curve had the good fortune to appear at a time when mathematics was being developed very rapidly and perhaps mathematicians were fortunate that so useful a curve appeared at this time. A new and powerful tool for the study of curves was furnished by the analytic geometry, whose year of birth is commonly given as 1637. New methods for finding tangents to curves, the areas under curves, and the volumes of solids bounded by curved surfaces were being discovered at a rapid pace, and a new subject, the calculus, was in the making. In these developments the cycloid was the one curve used preeminently and nearly every mathematician of the time used it in a trial of some of his new theory, even to the extent that much of the early histories of analytic geometry, calculus, and the cycloid are closely interwoven.

In the history that follows we shall not be concerned with historical minutiae, but only with the broad outlines of the story of this curve.

Early history of the curve

The original discoverer of the cycloid appears to be unknown.