In the twenty-ninth volume of the Society's Transactions, at page 59, Lord Brouncker's process for finding the ratio of two quantities (commonly known as the method of continued fractions) is extended to the comparison of three or more magnitudes. It is there shown that recurrence, which was believed to belong exclusively to equations of the second degree, extends to those of higher orders, and examples of this extension are given in determining the proportions of the heptagon and enneagon.