The seventeenth century saw a great acceleration in the development of mathematics. In particular, it witnessed the invention of analytic geometry and the calculus, achievements accomplished through the work of numerous mathematicians. The articles in this section deal with many aspects of these important ideas. In addition, several of the articles emphasize the relationship of history to the teaching of mathematics.

The age of exploration in Europe required new and better maps. The most famous of these, produced by Gerardus Mercator in 1569, enabled sailors to plot routes of fixed compass directions as straight lines. To accomplish this, Mercator progressively increased the distances between parallels of latitude, the further they were from the equator. But Mercator himself did not explain the mathematics behind this increase in distance. In their article, Fred Rickey and Philip Tuchinsky provide this explanation, basing their work on Edward Wright's Certaine Errors in Navigation of 1599, and relate it to the computation of the integral of the secant.

In the next article, E. A. Whitman explores the history of the cycloid. This curve, first described by Galileo, was used as a test case for the numerous new techniques being developed in the first half of the seventeenth century. Thus, Roberval found the area under the curve; Roberval, Fermat, and Descartes each found ways of drawing tangents to it; and Pascal found centers of gravity of both the region bounded by the curve and the solid formed by revolving a part of the curve around a line in the plane.