Overview

Eighteenth-century mathematicians enjoyed a vastly expanded set of techniques that could be applied to the study of curves and surfaces and a vastly expanded set of reasons to study them. Problems of projectile and planetary motion required a renewed understanding of the conic sections. Problems from engineering and the need for accurate maps of Earth's curved surface drew special attention to the general problems of representing curves and surfaces by equations. The researches of Jacob Hermann, Leonhard Euler, Gaspard Monge, and others would lead to the new disciplines of descriptive and differential geometry.

Background

The ancient Greeks had a good understanding of those curves generated by the conic sections—the hyperbola, parabola, ellipse, and circle—but from a geometrical perspective only. With the invention of analytic geometry by the French mathematician and philosopher...