As the eighteenth century drew to a close, mathematics was in a state of rapid change. New areas of mathematics remained wide open to research, while older, established areas of mathematics were finding new applications. Advances in analytic geometry, differential geometry, and algebra all played important roles in the development of mathematics in the eighteenth century. It was calculus, however, which commanded most of the attention of eighteenth-century mathematicians. Discovered by Isaac Newton (1642-1727) and Gottfried Leibniz (1646-1716) late in the seventeenth century, the theory and applications of calculus dominated the mathematical scene throughout the eighteenth century. New methods in calculus were developed by some of the greatest mathematicians in history: Newton, Leibniz, brothers Jakob Bernoulli (1654-1705) and Johann Bernoulli (1667-1748), Leonhard Euler (1707-1783), Joseph Louis Lagrange (1736-1813), and Pierre Simon Laplace (1749-1827), to name a few. However, as these techniques and applications of...