Analytic Geometry

During the seventeenth century, finding the solution to problems involving curves became important to industry and science. In astronomy, the slow acceptance of the heliocentric theory (Sun-centered theory) of planetary motion required mathematical formulas that would predict elliptical orbits. Other areas such as optics, navigation, and the military required formulas for things such as determining the curvature of a lens, the shortest route to a destination, and the trajectory of a cannon ball. Although the Greeks had developed hundreds of theorems related to curves, these did not provide quantitative values so they were not useful for practical applications. Consequently, many seventeenth-century mathematicians devoted their attention to the quantitative evaluation of curves. Two French mathematicians, Rene Descartes (1596-1650) and Pierre de Fermat (1601-1665) independently developed the foundations for analytic geometry. Descartes was first to publish his methods in an appendix titled La geometrie of his book Discours de la methode (1637).