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Mathematical Treasure: Works of Isaac Newton

Frank J. Swetz (The Pennsylvania State University)

Analysis per Quantitatum Series, Fluxiones, ac Differentias (1711) is a compilation of a selection of some of Isaac Newton’s works. It includes four separate treatises and a collection of correspondence.

The “Index” lists the specific contents. Of the four treatises, perhaps the most influential is “De Analysi per Aequationes Infinitas,” which was the first systematic discussion of calculus by Newton made available to the public. It was originally written in 1669. “Methodus Differentialis” contains what would eventually come to be known as the “Newton-Sterling Formulae.”


The first three pages of “De Analysi…”.

On page 5, Newton considers more difficult situations. Using the positive branch of the hyperbola \( y = \frac{a^2}{b+x} \), he employs division to expand the function into a series.

Here is an excerpt of a letter dated June 13, 1676, from Newton to Henry Oldenburg (ca.1615–1677), then Secretary of the Royal Society. Newton and Oldenburg were frequent correspondents.

These images are presented through the courtesy of the Lilly Library, Indiana University, Bloomington, Indiana.

Index to Mathematical Treasures

Frank J. Swetz (The Pennsylvania State University), "Mathematical Treasure: Works of Isaac Newton," Convergence (August 2019)