Descartes, Leibniz, and Newton on Analysis and Synthesis

Early modern European mathematicians understood the terms “analysis” and “synthesis” according to the definitions provided by Pappus in the Collectiones mathematicae, which had been available in Latin translation since 1588. This chapter surveys the meanings that the two Pappusian methods acquired in the works of Descartes, Leibniz, and Newton to appreciate the different approaches that these authors adopted to the new symbolical analytical methods of algebra and calculus and to the synthetic tracing of curves. Tracing curves was important not only for the construction of geometrical solutions but also for several practical applications.