The Fourth Root of 2,741,583,974

Abstract

This Primary Source Project is intended to introduce the Newton-Raphson method of approximating real roots of a function, based on Joseph Raphson's Analysis aequationum universalis, first published in 1690.  The readings and tasks in the first section project shepherd students into uncovering Raphson’s approach through a close reading of his original text (in translation), verification and scrutiny of his claims, and working through his examples. Then, students work through the iterative approximation method using the modern approach and notation with the aid of appropriate illustrations. Finally, they are presented with an opportunity to be guided through a series of coding tasks via a specially designed supplement. This project is suitable for use in a first-semester calculus course.