# 1911 Encyclopædia Britannica/Cotes, Roger

**COTES, ROGER** (1682–1716), English mathematician and
philosopher, was born on the 10th of July 1682 at Burbage,
Leicestershire, of which place his father, the Rev. Robert Cotes,
was rector. He was educated at Leicester school, and afterward
at St Paul's school, London. Proceeding to Trinity College,
Cambridge, in 1699, he obtained a fellowship in 1705, and in the
following year was appointed Plumian professor of astronomy
and experimental philosophy in the university of Cambridge.
He took orders in 1713; and the same year, at the request of Dr
Richard Bentley, he published the second edition of Newton's
*Principia* with an original preface. He died on the 5th of June
1716, leaving unfinished a series of elaborate researches on optics,
and a large amount of unpublished manuscript. He contributed
two memoirs to the *Philosophical Transactions*, one, "Logometria,"
which discusses the calculation of logarithms and
certain applications of the infinitesimal calculus, the other, a
"Description of the great fiery meteor seen on March 6th, 1716."
After his death his papers were collected and published by his
cousin and successor in the Plumian chair, Dr Robert Smith,
under the title *Harmonia Mensurarum* (1722). This work
included the "Logometria," the trigonometrical theorem known
as "Cote's Theorem on the Circle" (see Trigonometry), his
theorem on harmonic means, subsequently developed by Colin
Maclaurin, and a discussion of the curves known as "Cotes'
Spirals," which occur as the path of a particle described under the
influence of a central force varying inversely as the cube of the
distance. In 1738 Dr Robert Smith published Cotes' *Hydrostatical*
*and Pneumatical Lectures*, a work which was held in great
estimation. The exceptional genius of Cotes earned encomiums
from both his contemporaries and successors; Sir Isaac Newton
said, "If Mr Cotes had lived, we should have known something."