Brouncker
# William Brouncker

### Born: 1620
in Castle Lyons, Ireland

Died: 5 April 1684
in Oxford, England

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**William Brouncker,** Second Viscount Brouncker of Castle Lyons, was a founder and the first president (1662-1677) of the Royal Society of London.

Brouncker graduated from Oxford University in 1647, and was president of Gresham College, London from 1664 to 1667.
Brouncker's mathematical achievements include work on continued fractions and calculating logarithms by infinite series.

In 1655 he gave a continued fraction expansion of

Wallis told Huygens of this result and Huygens doubted that it was true. However after Brouncker correctly computed the first 10 places in the decimal expansion of ¹ using this formula, Huygens accepted the result.
Probably also in 1665 Brouncker computed the quadrature of the hyperbola although he did not publish this result until 1668.

Brouncker gave a method of solution to the diophantine equation

x - ay = 1

which evolved in a series of letters during 1657-58 and which first appears in Fermat's work. This was named Pell's equation by Euler who believed Pell, rather than Brouncker, had given the method of solution.
In 1659 Brouncker's improvement of Neile's computation of the arc length of the semicubical parabola ay = x appeared in Wallis's work.

Brouncker published only one book, a translation of Descartes' Musicae compendium (1653). Most of Brouncker's work was done with John Wallis and appeared in the publications of Wallis.

Brouncker also wrote a treatise on the Recoil of guns .

Samuel Pepys thought that Brouncker had treated Mrs Turner, one of his lady friends, badly and wrote in his diary

I perceive he is a rotten-hearted, false man as any I know ... and, therefore, I must beware of him accordingly, and I hope I shall.

**References (4 books/articles)**
**References elsewhere in this archive:**

Tell me about Pell's equation

William Brouncker was elected to the Royal Society of London in 1663. You can see a history of the Royal Society and a list of the members among the mathematicians in our archive

**Other Web sites:**

Rice University, USA

JOC/EFR December 1996