Jan Hudde’s Second Letter: On Maxima and Minima

Translated into English, with a Brief Introduction

Overview

In 1658, Jan Hudde extended Descartes’ fundamental idea for finding maxima and minima, namely that near the maximum value of a quantity the variable giving that quantity has two different values, but at the maximum these two values become one – algebraically a double root. He introduced more efficient ways of calculating double roots for polynomials and rational functions. His approach was the precursor of ours, equivalent to setting the formal derivative equal to zero, but his procedures were completely algebraic and based on a clever use of arithmetic progressions. Hudde also presented an early version of the Quotient Rule.

Hudde accomplished all of this in a letter written to Frans van Schooten in 1658, the second of two letters from Hudde that would appear in van Schooten's Latin edtion of Descartes' Geometria in 1659. Download the author's translation of Hudde's Second Letter.